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  • Correction to: Davenport constant for semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-10-15
    Guoqing Wang

    Given a finite commutative semigroup (written additively), denote by

    更新日期:2020-10-16
  • Existence of asymptotically almost periodic solutions for some second-order hyperbolic integrodifferential equations
    Semigroup Forum (IF 0.448) Pub Date : 2020-10-14
    Toka Diagana, Jamilu H. Hassan, Salim A. Messaoudi

    In this paper we study and obtain the existence of asymptotically almost periodic solutions to some classes of second-order hyperbolic integrodifferential equations of Gurtin–Pipkin type in a separable Hilbert space H. To illustrate our abstract results, the existence of asymptotically almost periodic mild solutions to the well-known Kirchoff plate equation is studied.

    更新日期:2020-10-14
  • On norm continuity, differentiability and compactness of perturbed semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-10-09
    A. Boulouz, H. Bounit, A. Driouich, S. Hadd

    The main purpose of this paper is to treat semigroup properties like norm continuity, compactness and differentiability for perturbed semigroups in Banach spaces. In particular, we investigate three large classes of perturbations: Miyadera–Voigt, Desch–Schappacher and Staffans–Weiss perturbations. Our approach is mainly based on feedback theory of Salamon–Weiss systems. Our results are applied to abstract

    更新日期:2020-10-11
  • Analysis of a non-linear model of populations structured by size
    Semigroup Forum (IF 0.448) Pub Date : 2020-10-07
    Anna Lo Grasso, Silvia Totaro

    The model we study deals with a population of marine invertebrates structured by size whose life stage is composed of adults and pelagic larvae such as barnacles contained in a local habitat. We prove existence and uniqueness of a continuous positive global mild solution and we give an estimate of it. We prove also that this solution is the strong solution of the problem.

    更新日期:2020-10-07
  • DTC ultrafilters on groups
    Semigroup Forum (IF 0.448) Pub Date : 2020-10-06
    Jan Pachl, Juris Steprāns

    We say that an ultrafilter on an infinite group G is DTC if it determines the topological centre of the semigroup \(\beta G\). If G has a subgroup of finite index in which conjugacy classes are all finite and uniformly bounded in size, then G does not admit a DTC ultrafilter. On the other hand, if G has no subgroup of finite index in which all conjugacy classes are finite, then G does admit a DTC ultrafilter

    更新日期:2020-10-07
  • Asymptotic behaviour of fast diffusions on graphs
    Semigroup Forum (IF 0.448) Pub Date : 2020-09-30
    Adam Gregosiewicz

    We study a diffusion process on a finite graph with semipermeable membranes on vertices. We prove, in \(L^1\) and \(L^2\)-type spaces that for a large class of boundary conditions, describing communication between the edges of the graph, the process is governed by a strongly continuous semigroup of operators, and we describe asymptotic behaviour of the diffusion semigroup as the diffusions’ speed increases

    更新日期:2020-10-02
  • Coverages on inverse semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-09-30
    Gilles G. de Castro

    First we give a definition of a coverage on an inverse semigroup that is weaker than the one given by Lawson and Lenz and that generalizes the definition of a coverage on a semilattice given by Johnstone. Given such a coverage, we prove that there exists a pseudogroup that is universal in the sense that it transforms cover-to-join idempotent-pure maps into idempotent-pure pseudogroup homomorphisms

    更新日期:2020-10-02
  • Basis reduction for cryptogroups and orthogroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-09-14
    Ana Casimiro, Eduardo Skapinakis

    The goal of this note is to provide equivalent bases of identities for subvarieties of completely regular semigroups.

    更新日期:2020-09-15
  • Multi-sensitivity with respect to a vector for semiflows
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-31
    Rahul Thakur, Ruchi Das

    The notions of multi-sensitivity with respect to a vector, \({\mathscr {N}}\)-sensitivity and strong multi-sensitivity are introduced and studied on semiflows under the action of the most general possible semigroups. Using the concept of Furstenberg families, some other stronger forms of sensitivity are also studied. Moreover, all these notions are studied on hyperspaces and on the product of semiflows

    更新日期:2020-09-01
  • $$\lambda $$ λ -Semidirect products of inverse monoids are weakly schreier extensions
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-31
    Peter F. Faul

    A split extension of monoids with kernel \(k :N \rightarrow G\), cokernel \(e :G \rightarrow H\) and splitting \(s :H \rightarrow G\) is weakly Schreier if each element \(g \in G\) can be written \(g = k(n)se(g)\) for some \(n \in N\). The characterization of weakly Schreier extensions allows them to be viewed as something akin to a weak semidirect product. The motivating examples of such extensions

    更新日期:2020-09-01
  • The $${\mathcal {F}}$$ F -transitivity and recurrence of translation semigroups on complex sectors
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-19
    Shengnan He, Xiaoli Sun, Mingqing Xiao

    In this paper, we study the \({\mathcal {F}}\)-transitive behaviour of the translation semigroups on complex sectors, where \({\mathcal {F}}\) is a Furstenberg family of the semigroup. We present the characterizations for \({\mathcal {F}}\)-transitive translation semigroups on complex sectors, which implies that the \({\mathcal {F}}\)-transitivity equals the thickly \({\mathcal {F}}\)-transitivity

    更新日期:2020-08-20
  • On graph inverse semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-18
    John Meakin, Zhengpan Wang

    We study the relationship between the graph inverse semigroups of two graphs when there is a directed immersion between the graphs and we provide structural information about graph inverse semigroups of finite graphs that admit a directed cover onto a bouquet of circles. We provide a topological characterization of the universal groups of the local submonoids of a graph inverse semigroup. We also find

    更新日期:2020-08-19
  • Relationships among quasivarieties induced by the min networks on inverse semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-14
    Ying-Ying Feng, Li-Min Wang, Zhi-Yong Zhou

    A congruence on an inverse semigroup S is determined uniquely by its kernel and trace. Denoting by \(\rho _k\) and \(\rho _t\) the least congruence on S having the same kernel and the same trace as \(\rho\), respectively, and denoting by \(\omega\) the universal congruence on S, we consider the sequence \(\omega\), \(\omega _k\), \(\omega _t\), \((\omega _k)_t\), \((\omega _t)_k\), \(((\omega _k)_t)_k\)

    更新日期:2020-08-15
  • On finitary properties for fiber products of free semigroups and free monoids
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-14
    Ashley Clayton

    We consider necessary and sufficient conditions for finite generation and finite presentability for fiber products of free semigroups and free monoids. We give a necessary and sufficient condition on finite fiber quotients for a fiber product of two free monoids to be finitely generated, and show that all such fiber products are also finitely presented. By way of contrast, we show that fiber products

    更新日期:2020-08-15
  • Right ideal Howson semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-07
    Scott Carson, Victoria Gould

    We define a semigroup S to be right ideal Howson if the intersection of any two finitely generated right ideals, or, equivalently, any two principal right ideals, is again finitely generated. We give many examples of such semigroups, including right coherent monoids, finitely aligned semigroups, and inverse semigroups. We investigate the closure of the class of right ideal Howson semigroups under algebraic

    更新日期:2020-08-08
  • A note on dual prehomomorphisms from a group into the Margolis–Meakin expansion of a group
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-07
    Bernd Billhardt, Boorapa Singha, Worachead Sommanee, Paweena Thamkaew, Jukrapong Tiammee

    We give a category-free order theoretic variant of a key result in Auinger and Szendrei (J Pure Appl Algebra 204(3):493–506, 2006) and illustrate how it might be used to compute whether a finite X-generated group H admits a canonical dual prehomomorphism into the Margolis–Meakin expansion M(G) of a finite X-generated group G. We show that for G the Klein four-group a suitable H must be of exponent

    更新日期:2020-08-08
  • Near-ring congruences on additively regular seminearrings
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-05
    Kamalika Chakraborty, Pavel Pal, Sujit Kumar Sardar

    In this paper we first obtain analogues of some results of LaTorre (Semigroup Forum 24(1):327–340, 1982) in the setting of additively regular seminearrings which in turn not only give rise to refinements of some important results viz. Propositions 3.16, 3.17, Theorem 3.20 of Sardar and Mukherjee (Semigroup Forum 93(3):629–631, 2016) and Theorem 3.22 of Sardar and Mukherjee (Semigroup Forum 88(3):541–554

    更新日期:2020-08-06
  • Gluing semigroups: when and how
    Semigroup Forum (IF 0.448) Pub Date : 2020-08-04
    Philippe Gimenez, Hema Srinivasan

    Given two semigroups \(\langle A\rangle\) and \(\langle B\rangle\) in \({\mathbb {N}}^n\), we wonder when they can be glued, i.e., when there exists a semigroup \(\langle C\rangle\) in \({\mathbb {N}}^n\) such that the defining ideals of the corresponding semigroup rings satisfy that \(I_C=I_A+I_B+\langle \rho \rangle\) for some binomial \(\rho\). If \(n\ge 2\) and \(k[A]\) and \(k[B]\) are Cohen–Macaulay

    更新日期:2020-08-04
  • The Bohr compactification of an abelian group as a quotient of its Stone–Čech compactification
    Semigroup Forum (IF 0.448) Pub Date : 2020-07-29
    Pavol Zlatoš

    We will prove that, for any abelian group G, the canonical (surjective and continuous) mapping \(\varvec{\beta }G\rightarrow \mathfrak {b}G\) from the Stone–Čech compactification \(\varvec{\beta }G\) of G to its Bohr compactification \(\mathfrak {b}G\) is a homomorphism with respect to the semigroup operation on \(\varvec{\beta }G\), extending the multiplication on G, and the group operation on \(\mathfrak

    更新日期:2020-07-30
  • On the spectra of commutative semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-07-27
    Huanrong Wu, Qingguo Li

    This study aims to investigate the Zariski topology on the prime ideals of a commutative semigroup S, denoted by Spec(S). First, we show that a topological space X is homeomorphic to Spec(S) for some commutative semigroup S if and only if X is an SS-space that can be described purely in topological terms. Next, we show that an adjunction exists between the category of commutative semigroups and that

    更新日期:2020-07-28
  • How to generalise demonic composition
    Semigroup Forum (IF 0.448) Pub Date : 2020-07-15
    Tim Stokes

    Demonic composition is defined on the set of binary relations over the non-empty set X, \(Rel_X\), and is a variant of standard or “angelic” composition. It arises naturally in the setting of the theory of non-deterministic computer programs, and shares many of the nice features of ordinary composition (it is associative, and generalises composition of functions). When equipped with the operations

    更新日期:2020-07-16
  • Semigroups of partial transformations with kernel and image restricted by an equivalence
    Semigroup Forum (IF 0.448) Pub Date : 2020-07-03
    Jorge André, Janusz Konieczny

    For an arbitrary set X and an equivalence relation \(\mu\) on X, denote by \(P_\mu (X)\) the semigroup of partial transformations \(\alpha\) on X such that \(x\mu \subseteq x(\ker (\alpha ))\) for every \(x\in {{\,\mathrm{dom}\,}}(\alpha )\), and the image of \(\alpha\) is a partial transversal of \(\mu\). Every transversal K of \(\mu\) defines a subgroup \(G=G_{K}\) of \(P_\mu (X)\). We study subsemigroups

    更新日期:2020-07-03
  • On the structure theory of partial automaton semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-07-03
    Daniele D’Angeli, Emanuele Rodaro, Jan Philipp Wächter

    We study automaton structures, i.e., groups, monoids and semigroups generated by an automaton, which, in this context, means a deterministic finite-state letter-to-letter transducer. Instead of considering only complete automata, we specifically investigate semigroups generated by partial automata. First, we show that the class of semigroups generated by partial automata coincides with the class of

    更新日期:2020-07-03
  • The commutative cohomology of nilmonoids, revisited
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-29
    Pierre Antoine Grillet

    A nilmonoid is a nilsemigroup N with an identity element adjoined. New properties of the canonical presentation of N yield a more precise characterization of 2-cocycles, improvements in the computation of the cohomology of N, and a universal coefficients theorem.

    更新日期:2020-06-30
  • The classification of maximal inverse monoids of matrices
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-24
    Bing Duan, Wen Ting Zhang, Yan Feng Luo

    Let \({\mathbb {F}}\) be a field. The set \(M_{n}({\mathbb {F}})\) of all \(n \times n\) matrices over \({\mathbb {F}}\) forms a monoid under usual matrix multiplication. We explore and classify all maximal inverse monoids in \(M_{n}({\mathbb {F}})\). Given a partition of \(\{1,\ldots ,n\}\), we construct a maximal matrix inverse monoid as a direct sum of some block matrices and show that every maximal

    更新日期:2020-06-25
  • Finite monogenic semigroups and saturated varieties of semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-16
    Shabir Ahmad Ahanger

    J. M. Howie has shown that the finite monogenic semigroups are absolutely closed. We provide a new, simple and direct proof of Howie’s result. We also show that all the varieties defined by the identities ax = axa, axy = axay and axy = axyay are saturated if and only if they are epimorphically closed.

    更新日期:2020-06-16
  • Applications of the Hales–Jewett theorem near zero
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-15
    Pintu Debnath, Sayan Goswami

    The famous van der Waerden’s theorem states that if \({\mathbb{N}}\) is finitely colored then one color class will contain arithmetic progressions of arbitrary length. The polynomial van der Waerden’s theorem says that if \(p_{1}(x),p_2(x),\ldots ,p_{k}(x)\) are polynomials with integer coefficients and zero constant term and \({\mathbb{N}}\) is finitely colored, then there exist \(a,d\in {\mathbb{N}}\)

    更新日期:2020-06-15
  • Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-10
    Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov

    In this paper we describe the Euler semigroup \(\{e^{-t\mathbb {E}^{*}\mathbb {E}}\}_{t>0}\) on homogeneous Lie groups, which allows us to obtain various types of the Hardy–Sobolev and Gagliardo–Nirenberg type inequalities for the Euler operator \(\mathbb {E}\). Moreover, the sharp remainder terms of the Sobolev type inequality, maximal Hardy inequality and \(|\cdot |\)-radial weighted Hardy–Sobolev

    更新日期:2020-06-10
  • On module cohomology of the Fourier algebra of an inverse semigroup
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-09
    Abasalt Bodaghi, Reza Rezavand

    For an inverse semigroup S with the set of idempotents E, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character amenable, module (operator) biflat and module (operator) biprojective (as \(l^1(E)\)-module). Some examples show that when S is either a bicyclic inverse semigroup or a Brandt inverse semigroup, A(S) is module amenable, module biprojective

    更新日期:2020-06-09
  • Semiring varieties related to multiplicative Green’s relations on a semiring
    Semigroup Forum (IF 0.448) Pub Date : 2020-06-05
    Yanliang Cheng, Yong Shao

    In this paper, by means of congruence openings of multiplicative Green’s relations on a semiring we define and study several varieties of semirings, obtain the relationship between these varieties and give Mal’cev product decompositions of some varieties of idempotent semirings. In particular, we establish order embeddings of the lattice of all subvarieties of the variety of multiplicatively idempotent

    更新日期:2020-06-05
  • Numerical semigroups generated by primes
    Semigroup Forum (IF 0.448) Pub Date : 2020-05-28
    Michael Hellus, Anton Rechenauer, Rolf Waldi

    Let \(p_1=2, p_2=3, p_3=5, \ldots\) be the consecutive prime numbers, \(S_n\) the numerical semigroup generated by the primes not less than \(p_n\) and \(u_n\) the largest irredundant generator of \(S_n\). We will show, that \(u_n\sim 3p_n\). Similarly, for the largest integer \(f_n\) not contained in \(S_n\), by computational evidence (https://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/Hellus/table_1

    更新日期:2020-05-28
  • Semigroup and Riesz transform for the Dunkl–Schrödinger operators
    Semigroup Forum (IF 0.448) Pub Date : 2020-05-28
    Béchir Amri, Amel Hammi

    Let \(L_k=-\Delta _k+V\) be the Dunkl–Schrödinger operators, where \(\Delta _k=\sum _{j=1}^dT_j^2\) is the Dunkl Laplace operator associated to the Dunkl operators \(T_j\) on \(\mathbb {R}^d\) and V is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform \(R_j= T_j L_k^{-1/2}\) as a \(L^2\)-bounded operator and we first prove that it is of weak type (1

    更新日期:2020-05-28
  • Simple semirings with right multiplicatively absorbing elements
    Semigroup Forum (IF 0.448) Pub Date : 2020-05-27
    Barbora Batíková, Tomáš Kepka, Petr Němec

    We investigate (congruence-simple) semirings with at least two right multiplicatively absorbing elements, using left semimodules.

    更新日期:2020-05-27
  • Simple semirings with a bi-absorbing element
    Semigroup Forum (IF 0.448) Pub Date : 2020-05-13
    Tomáš Kepka, Miroslav Korbelář, Petr Němec

    We study additively idempotent congruence-simple semirings with a bi-absorbing element. We characterize a subclass of these semirings in terms of semimodules of a special type (o-characteristic semimodules). We show that o-characteristic semimodules are uniquely determined. We also generalize a result by Ježek and Kepka on simple semirings of endomorphisms of semilattices.

    更新日期:2020-05-13
  • Almost periodicity and ergodic theorems for nonexpansive mappings and semigroups in Hadamard spaces
    Semigroup Forum (IF 0.448) Pub Date : 2020-05-06
    Hadi Khatibzadeh, Hadi Pouladi

    The main purpose of this paper is to prove the mean ergodic theorem for nonexpansive mappings and semigroups in locally compact Hadamard spaces, including finite dimensional Hadamard manifolds. The main tool for proving ergodic convergence is the almost periodicity of orbits of a nonexpansive mapping. Therefore, in the first part of the paper, we study almost periodicity (and as a special case, periodicity)

    更新日期:2020-05-06
  • On atomic and unsplitable endofunctions
    Semigroup Forum (IF 0.448) Pub Date : 2020-04-29
    Teresa Xueshan Li

    In the study of a cocommutative Hopf algebra PFSym built on parking functions, the author presented two free generating sets of PFSym which are indexed by atomic parking functions and unsplitable parking functions. The notions of atomic parking function and unsplitable parking function are introduced via two binary operations called the slash product and the split product respectively. It follows that

    更新日期:2020-04-29
  • Set-theoretical solutions of the Yang–Baxter and pentagon equations on semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-04-21
    Francesco Catino, Marzia Mazzotta, Paola Stefanelli

    The Yang–Baxter and pentagon equations are two well-known equations of Mathematical Physic. If S is a set, a map \(s:S\times S\rightarrow S\times S\) is said to be a set-theoretical solution of the quantum Yang–Baxter equation if $$\begin{aligned} s_{23}\, s_{13}\, s_{12} = s_{12}\, s_{13}\, s_{23}, \end{aligned}$$ where \(s_{12}=s\times {{\,\mathrm{id}\,}}_S\), \(s_{23}={{\,\mathrm{id}\,}}_S\times

    更新日期:2020-04-21
  • On nilpotent subsemigroups of the order-preserving and decreasing transformation semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-03-23
    Melek Yağcı, Emrah Korkmaz

    Let \({\mathcal {C}}_{n}\) be the semigroup of all order-preserving and decreasing transformations on \(X_{n}=\{1,\ldots ,n\}\) under its natural order, and let \(N({\mathcal {C}}_{n})\) be the subsemigroup of all nilpotent elements of \({\mathcal {C}}_{n}\). In this paper we determine the minimum generating set of \(N({\mathcal {C}}_n)\), and so the rank of \(N({\mathcal {C}}_n)\). Moreover, we investigate

    更新日期:2020-03-23
  • Some results on $$\mathcal {L}$$ L -commutative semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-03-19
    Roman S. Gigoń

    We prove first that every \(\mathcal {H}\)-commutative semigroup is stable. Using this result [and some results from the standard text (Nagy, Special classes of semigroups, Kluwer, Dordrecht, 2001)], we give two equivalent conditions for a semigroup to be an archimedean \(\mathcal {H}\)-commutative semigroup containing an idempotent element. It turns out that this result can be partially extended to

    更新日期:2020-03-19
  • Finiteness spaces, étale groupoids and their convolution algebras
    Semigroup Forum (IF 0.448) Pub Date : 2020-03-12
    Joey Beauvais-Feisthauer, Richard Blute, Ian Dewan, Blair Drummond, Pierre-Alain Jacqmin

    Given a ring R, we extend Ehrhard’s linearization process by associating to any pre-finiteness space an R-module endowed with a Lefschetz topology. For a semigroup in the category of pre-finiteness spaces, one can endow this R-module with the convolution product to obtain an R-algebra. As examples of pre-finiteness spaces, we study topological spaces with bounded subsets (i.e., included in a compact)

    更新日期:2020-03-12
  • Commutation semigroups of finite metacyclic groups with trivial centre
    Semigroup Forum (IF 0.448) Pub Date : 2020-03-11
    Darien DeWolf, Charles C. Edmunds

    We study the right and left commutation semigroups of finite metacyclic groups with trivial centre. These are presented $$\begin{aligned} G(m,n,k) = \left\langle {a,b;{a^m} = 1,{b^n} = 1,{a^b} = {a^k}} \right\rangle \quad (m,n,k\in {\mathbb {Z}}^+) \end{aligned}$$ with \((m,k - 1) = 1\) and \(n = \mathrm {ind}_m(k),\) the smallest positive integer for which \({k^n} = 1\,\pmod m,\) with the conjugate

    更新日期:2020-03-11
  • Approximate semi-amenability of Banach algebras
    Semigroup Forum (IF 0.448) Pub Date : 2020-03-06
    F. Ghahramani, R. J. Loy

    In recent work of the authors the notion of a derivation being approximately semi-inner arose as a tool for investigating (approximate) amenability questions for Banach algebras. Here we investigate this property in its own right, together with the consequent one of approximately semi-amenability. Under certain hypotheses regarding approximate identities this new notion is the same as approximate amenability

    更新日期:2020-03-06
  • On the Ellis semigroup of a cascade on a compact metric countable space
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-27
    Andres Quintero, Carlos Uzcátegui

    Let X be a compact metric countable space, let \(f:X\rightarrow X\) be a homeomorphism and let E(X, f) be its Ellis semigroup. Among other results we show that the following statements are equivalent: (1) (X, f) is equicontinuous, (2) (X, f) is distal and (3) every point is periodic. We use this result to give a direct proof of a theorem of Ellis saying that (X, f) is distal if, and only if, E(X, f)

    更新日期:2020-02-27
  • The lattice of ai-semiring varieties satisfying $$x^n\approx x$$xn≈x and $$xy\approx yx$$xy≈yx
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-25
    Miaomiao Ren, Xianzhong Zhao, Yong Shao

    We study the lattice \({{\mathscr {L}}}({{\mathbf{CSr}}}(n, 1))\) of subvarieties of the ai-semiring variety \({{\mathbf{CSr}}}(n, 1)\) defined by \(x^n\approx x\) and \(xy\approx yx\). We divide \({{\mathscr {L}}}({{\mathbf{CSr}}}(n, 1))\) into five intervals and provide an explicit description of each member of these intervals except \([{{\mathbf{CSr}}}(2, 1), {\mathbf{CSr}}(n, 1)]\). Based on these

    更新日期:2020-02-25
  • Chaos, attraction, and control for semigroup actions
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-19
    Josiney A. Souza, Hélio V. M. Tozatti

    This manuscript studies sensitivity and chaos for semigroup actions on completely regular spaces. The main results explain how the notions of attraction and control play a fundamental role in the investigation of Auslander–Yorke and Li–Yorke chaos. A general type of non-chaotic semigroup action is exhibited and a criterium for chaos in control systems is presented.

    更新日期:2020-02-19
  • Representations of inverse semigroups in complete atomistic inverse meet-semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-18
    D. G. FitzGerald

    As an appropriate generalisation of the features of the classical (Schein) theory of representations of inverse semigroups in \({\mathscr {I}}_{X}\), a theory of representations of inverse semigroups by homomorphisms into complete atomistic inverse \(\wedge\)-semigroups is developed. This class of inverse \(\wedge\)-semigroups, otherwise known as inverse algebras, includes partial automorphism monoids

    更新日期:2020-02-18
  • Correction to: Some characterizations of the tensor product of complete lattices with applications to quantales
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-10
    Javier Gutiérrez García, Ulrich Höhle, Tomasz Kubiak

    The remaining part of the original proof of Corollary 2 remains unchanged.

    更新日期:2020-02-10
  • The universal minimal one parameter system with quasi-discrete spectrum
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-10
    F. Choobtarash, A. Jabbari

    The universal minimal one parameter system will be characterized as the space \(\Gamma ^{\infty }\), in which \(\Gamma\) is the Bohr compactification of the additive group \({\mathbb {R}}\) of real numbers. In this way, we need to show that \(\Gamma ^\infty\) is isomorphic to the spectrum of \(W({\mathbb {R}})\), the norm closure of the invariant algebra generated by the maps \(\exp q(t)\), where q(t)

    更新日期:2020-02-10
  • Regularity and Green’s relations on semigroups of transformations with restricted range that preserve an equivalence
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-07
    Kritsada Sangkhanan, Jintana Sanwong

    Let Y be a subset of X and T(X, Y) the set of all functions from X into Y. Then, under the operation of composition, T(X, Y) is a subsemigroup of the full transformation semigroup T(X). Let E be an equivalence on X. Define a subsemigroup \(T_E(X,Y)\) of T(X, Y) by $$\begin{aligned} T_E(X,Y)=\{\alpha \in T(X,Y):\forall (x,y)\in E, (x\alpha ,y\alpha )\in E\}. \end{aligned}$$ Then \(T_E(X,Y)\) is the

    更新日期:2020-02-07
  • Sensitivity, Devaney’s chaos and Li–Yorke $$\varepsilon $$ε -chaos
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-04
    Huoyun Wang, Qing Liu, Huahai Li, Heman Fu

    We consider the sensitivity from a topological point of view. We show that a continuous, topologically transitive and non-minimal action of a monoid S on an infinite \(T_4\) topological space which admits a dense set of almost periodic points is sensitive. We also prove that a uniformly continuous, topologically transitive and non-minimal action of a monoid S on an infinite Hausdorff uniform space

    更新日期:2020-02-04
  • Classifications of quasitrivial semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-02-04
    Jimmy Devillet, Jean-Luc Marichal, Bruno Teheux

    We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups, we address and solve several related enumeration problems.

    更新日期:2020-02-04
  • A generalization of Wilf’s conjecture for generalized numerical semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2020-01-21
    Carmelo Cisto, Michael DiPasquale, Gioia Failla, Zachary Flores, Chris Peterson, Rosanna Utano

    A numerical semigroup is a submonoid of \({\mathbb {N}}\) with finite complement in \({\mathbb {N}}\). A generalized numerical semigroup is a submonoid of \({\mathbb {N}}^{d}\) with finite complement in \({\mathbb {N}}^{d}\). In the context of numerical semigroups, Wilf’s conjecture is a long standing open problem whose study has led to new mathematics and new ways of thinking about monoids. A natural

    更新日期:2020-01-21
  • The structure of subdirectly irreducible and uniform acts over rectangular bands
    Semigroup Forum (IF 0.448) Pub Date : 2020-01-21
    Mojtaba Sedaghatjoo, Mohammad Roueentan

    The aim of this paper is characterising subdirectly irreducible acts over rectangular bands. Besides, we identify the structure of such acts, their bounds and all their non-isomorphic classes. Ultimately, our approach provides characterisation of uniform acts over rectangular bands as an overclass of subdirectly irreducible acts.

    更新日期:2020-01-21
  • A new example of a limit variety of monoids
    Semigroup Forum (IF 0.448) Pub Date : 2019-12-16
    S. V. Gusev

    A variety of universal algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. Until recently, only two explicit examples of limit varieties of monoids, constructed by Jackson, were known. Recently Zhang and Luo found the third example of such a variety. In our work, one more example of a limit variety of monoids is given.

    更新日期:2019-12-16
  • Refinement monoids and adaptable separated graphs
    Semigroup Forum (IF 0.448) Pub Date : 2019-12-11
    Pere Ara, Joan Bosa, Enrique Pardo

    We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I-systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide

    更新日期:2019-12-11
  • A note on the norm-continuity for evolution families arising from non-autonomous forms
    Semigroup Forum (IF 0.448) Pub Date : 2019-12-09
    Omar EL-Mennaoui, Hafida Laasri

    We consider evolution equations of the form $$\begin{aligned} \dot{u}(t)+{\mathcal {A}}(t)u(t)=0,\ \ t\in [0,T],\ \ u(0)=u_0, \end{aligned}$$ where \({\mathcal {A}}(t),\ t\in [0,T],\) are associated with a non-autonomous sesquilinear form \({\mathfrak {a}}(t,\cdot ,\cdot )\) on a Hilbert space H with constant domain \(V\subset H.\) In this note we continue the study of fundamental operator theoretical

    更新日期:2019-12-09
  • On some intervals of varieties of completely regular semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-12-02
    Mario Petrich

    Completely regular semigroups with the unary operation of inversion within their maximal subgroups form a variety under inclusion denoted by \(\mathcal {C}\mathcal {R}\). The lattice of its subvarieties is denoted by \(\mathcal {L}(\mathcal {C}\mathcal {R})\). Kernel, trace, left trace and right trace relations on \(\mathcal {L}(\mathcal {C}\mathcal {R})\) induce operators which can be used to produce

    更新日期:2019-12-02
  • Cancellative conjugation semigroups and monoids
    Semigroup Forum (IF 0.448) Pub Date : 2019-11-21
    A. P. Garrão, N. Martins-Ferreira, M. Raposo, M. Sobral

    We show that the category of cancellative conjugation semigroups is weakly Mal’tsev and give a characterization of all admissible diagrams there. In the category of cancellative conjugation monoids we describe, for Schreier split epimorphisms with codomain B and kernel X, all morphisms \(h:X\rightarrow B\) which induce a reflexive graph, an internal category or an internal groupoid. We describe Schreier

    更新日期:2019-11-21
  • Relationship among several types of sensitivity in general semi-flows
    Semigroup Forum (IF 0.448) Pub Date : 2019-11-20
    Xinxing Wu, Xu Zhang

    In this paper, we show that there exists a monoid, on which neither the syndetic property nor the dual syndetic property holds, and there exists a strongly mixing semi-flow with this monoid action which does not have thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, or thickly periodical sensitivity. Meanwhile, we show that there exists a thickly sensitive cascade which is not

    更新日期:2019-11-20
  • Commutative monoids and their corresponding affine $$\Bbbk $$ k -schemes
    Semigroup Forum (IF 0.448) Pub Date : 2019-11-19
    Alberto Navarro, José Navarro, Ignacio Ojeda

    In this expository note, we give a self-contained presentation of the equivalence between the opposite category of commutative monoids and that of commutative, monoid \(\Bbbk \)-schemes that are diagonalizable, for any field \(\Bbbk \).

    更新日期:2019-11-19
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