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  • 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
  • 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
  • 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
  • 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 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
  • Decay of the local energy for the solutions of the critical Klein–Gordon equation
    Semigroup Forum (IF 0.448) Pub Date : 2019-11-19
    Ahmed Bchatnia, Naima Mehenaoui

    We prove the exponential decay of local energy for the Klein–Gordon equation with localized critical nonlinearity. The proof relies on generalized Strichartz estimates, and semi-group of Lax–Phillips.

    更新日期:2019-11-19
  • Epimorphisms, dominions and varieties of bands
    Semigroup Forum (IF 0.448) Pub Date : 2019-09-30
    Shabir Ahmad Ahanger, Aftab Hussain Shah

    We show that all subvarieties of left regular bands are closed in the variety of all bands. We also show that all subvarieties of left seminormal bands are saturated in the variety of all bands which shows that, in the category of all bands, any epi from a left seminormal band is surjective.

    更新日期:2019-09-30
  • Analysis on semihypergroups: function spaces, homomorphisms and ideals
    Semigroup Forum (IF 0.448) Pub Date : 2019-09-28
    Choiti Bandyopadhyay

    The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by Dunkl (Am Math Soc 179:331–348, 1973), Jewett (Adv Math 18(1):1–101, 1975) and Spector (Apercu de la theorie des hypergroups, (French) Analyse harmonique sur les groupes de Lie (Sém. Nancy–Strasbourg, 1973–75), Springer, New York, 1975) independently around 1972. We introduce and study several

    更新日期:2019-09-28
  • On images of complete topologized subsemilattices in sequential semitopological semilattices
    Semigroup Forum (IF 0.448) Pub Date : 2019-09-26
    Taras Banakh, Serhii Bardyla

    A topologized semilattice X is called complete if each non-empty chain \(C\subset X\) has \(\inf C\in {\bar{C}}\) and \(\sup C\in {\bar{C}}\). We prove that for any continuous homomorphism \(h:X\rightarrow Y\) from a complete topologized semilattice X to a sequential Hausdorff semitopological semilattice Y the image h(X) is closed in Y.

    更新日期:2019-09-26
  • Stability of the wave equations on a tree with local Kelvin–Voigt damping
    Semigroup Forum (IF 0.448) Pub Date : 2019-09-26
    Kaïs Ammari, Zhuangyi Liu, Farhat Shel

    In this paper we study the stability problem of a tree of elastic strings with local Kelvin–Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at the vertices of the tree, exponential/polynomial stability are proved. Our results generalize the case of single elastic string with local Kelvin–Voigt damping

    更新日期:2019-09-26
  • On the concept of digroup action
    Semigroup Forum (IF 0.448) Pub Date : 2019-09-16
    Harry Guzmán, Fausto Ongay

    In this work we introduce the concept of digroup action, and investigate some of its basic properties, such as the notion of orbits and stabilizers.

    更新日期:2019-09-16
  • Epimorphisms, dominions and $$\mathcal {H}$$H -commutative semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-08-21
    Noor Alam, Peter M. Higgins, Noor Mohammad Khan

    In the present paper, a series of results and examples that explore the structural features of \(\mathcal {H}\)-commutative semigroups are provided. We also generalize a result of Isbell from commutative semigroups to \(\mathcal {H}\)-commutative semigroups by showing that the dominion of an \(\mathcal {H}\)-commutative semigroup is \(\mathcal {H}\)-commutative. We then use this to generalize Howie

    更新日期:2019-08-21
  • On associative operations on commutative integral domains
    Semigroup Forum (IF 0.448) Pub Date : 2019-08-12
    Erkko Lehtonen, Florian Starke

    We describe the associative multilinear polynomial functions over commutative integral domains. This extends Marichal and Mathonet’s result on infinite integral domains and provides a new proof of Andres’s classification of two-element n-semigroups.

    更新日期:2019-08-12
  • Weak finitely regular relations and applications
    Semigroup Forum (IF 0.448) Pub Date : 2019-07-30
    Shuzhen Luo, Xiaoquan Xu

    In this note, we introduce the concepts of weak finitely regular relations and weak hypercontinuous posets. It is proved that when a binary relation \(\rho :X/\rightarrow Y\) satisfies a certain condition, \(\rho \) is weak finitely regular if and only if \((\varphi _{\rho }(X,Y),\subseteq )\) is a weak hypercontinuous poset. For a poset P, we get that the relation \(\not \le \) on P is weak finitely

    更新日期:2019-07-30
  • Hausdorff tight groupoids generalised
    Semigroup Forum (IF 0.448) Pub Date : 2019-06-13
    Tristan Bice, Charles Starling

    We extend Exel’s ample tight groupoid construction to general locally compact étale groupoids in the Hausdorff case. Moreover, we show how inverse semigroups are represented in this way as ‘pseudobases’ of open bisections, thus yielding a duality which encompasses various extensions of the classic Stone duality.

    更新日期:2019-06-13
  • Chain conditions on commutative monoids
    Semigroup Forum (IF 0.448) Pub Date : 2019-06-11
    Bijan Davvaz, Zahra Nazemian

    We consider commutative monoids with some kinds of isomorphism condition on their ideals. We say that a monoid S has isomorphism condition on its ascending chains of ideals, if for every ascending chain \(I_1 \subseteq I_2 \subseteq \cdots \) of ideals of S, there exists n such that \(I_i \cong I_n \), as S-acts, for every \(i \ge n\). Then S for short is called Iso-AC monoid. Dually, the concept of

    更新日期:2019-06-11
  • On zigzag maps and the path category of an inverse semigroup
    Semigroup Forum (IF 0.448) Pub Date : 2019-05-29
    Allan Donsig, Jennifer Gensler, Hannah King, David Milan, Ronen Wdowinski

    We study the path category of an inverse semigroup admitting unique maximal idempotents and give an abstract characterization of the inverse semigroups arising from zigzag maps on a left cancellative category. As applications we show that every inverse semigroup is Morita equivalent to an inverse semigroup of zigzag maps and hence the class of Cuntz–Krieger \(C^*\)-algebras of singly aligned categories

    更新日期:2019-05-29
  • Quasi-multipliers on Banach algebras related to locally compact semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-05-28
    A. Alinejad, M. Rostami

    Let \({\mathcal {S}}\) be a compactly cancellative foundation semigroup with identity and \(M_a({\mathcal {S}})\) be its semigroup algebra. In this paper, we give some characterizations for \( {{\mathfrak {Q}}}{{\mathfrak {M}}}(M_a({\mathcal {S}}))\), the quasi-multipliers of \(M_a({\mathcal {S}})\). It is shown that \( {{\mathfrak {Q}}}{{\mathfrak {M}}}(M_a({\mathcal {S}}))\) may be identified by

    更新日期:2019-05-28
  • Equivalence of $$L_p$$Lp diffusion approximation and a function’s diffusion smoothness
    Semigroup Forum (IF 0.448) Pub Date : 2019-05-28
    Maxim J. Goldberg, Seonja Kim

    Let \(\left\{ A_t\right\} _{t\ge 0}\) be a symmetric diffusion semigroup on \(L_p(X)\), for X a complete positive \(\sigma \)-finite measure space. We establish an equivalence between the \(L_p\) rate of approximation of \(A_t\phi \) to \(\phi \) (as \(t\rightarrow 0^+\)) and a measure of the smoothness of \(\phi \) relative to the diffusion. The following is our main result: For \(10\) independent

    更新日期:2019-05-28
  • On properties of square-free elements in commutative cancellative monoids
    Semigroup Forum (IF 0.448) Pub Date : 2019-05-06
    Piotr Jędrzejewicz, Mikołaj Marciniak, Łukasz Matysiak, Janusz Zieliński

    We discuss various square-free factorizations in monoids in the context of: atomicity, ascending chain condition for principal ideals, decomposition, and a greatest common divisor property. Moreover, we obtain a full characterization of submonoids of factorial monoids in which all square-free elements of a submonoid are square-free in a monoid. We also present a factorial property implying that all

    更新日期:2019-05-06
  • Larger locally compact monothetic semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-03-26
    Yevhen Zelenyuk

    We show that for every \(k\in {\mathbb {N}}\), there is a locally compact noncompact monothetic semigroup S with identity such that S is homeomorphic to a closed nowhere dense subset of \({\mathbb {R}}^{k+1}\) and the connected components of S are homeomorphic to \({\mathbb {R}}_+^k\), so \(\dim S=k\). The semigroup S can be algebraically embedded in \({\mathbb {R}}\) and cannot be topologically and

    更新日期:2019-03-26
  • Ramsey theory for hypergroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-02-26
    Vishvesh Kumar, Kenneth A. Ross, Ajit Iqbal Singh

    In this paper, Ramsey theory for discrete hypergroups is introduced with emphasis on polynomial hypergroups, discrete orbit hypergroups and hypergroup deformations of semigroups. In this context, new notions of Ramsey principle for hypergroups and \(\alpha \)-Ramsey hypergroups, \(0 \le \alpha <1,\) are defined and studied.

    更新日期:2019-02-26
  • Character inner amenability for semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-02-19
    Abasalt Bodaghi, Ali Jabbari, Massoud Amini

    Let \(\varphi \) be a character on a semigroup S. We introduce the notions of \(\varphi \)-inner amenability and character inner amenability for S. We study the relation between the character inner amenability of a discrete semigroup S and character inner amenability of \(\ell ^1(S)\). Applying this result, we give some examples to show that the class of character inner amenable semigroup algebras

    更新日期:2019-02-19
  • Combined algebraic properties of $$C^{*}$$C∗ -sets near zero
    Semigroup Forum (IF 0.448) Pub Date : 2019-02-19
    Tanumoy Bhattacharya, Sukrit Chakraborty, Sourav Kanti Patra

    It is known that for an \(IP^*\) set A in \({\mathbb {N}}\) and a sequence \(\langle {x_n}\rangle _{n=1}^{\infty }\) there exists a sum subsystem \(\langle {y_n}\rangle _{n=1}^{\infty }\) of \(\langle {x_n}\rangle _{n=1}^{\infty }\) such that \(FS\left( \langle {y_n}\rangle _{n=1}^{\infty }\right) \)\(\cup \)\(FP\left( \langle {y_n}\rangle _{n=1}^{\infty }\right) \subseteq A\). Similar types of results

    更新日期:2019-02-19
  • Characterization of distributive semigroup operations on the positive real numbers
    Semigroup Forum (IF 0.448) Pub Date : 2019-02-19
    Sin-Ei Takahasi, Takeshi Miura, Hirokazu Oka

    Given any cancellative continuous semigroup operation \(\star \) on the positive real numbers \(\mathbf {R}_+\) with the ordinary topology, we completely characterize the set \(\mathcal {D}_\star (\mathbf {R}_+)\) of all cancellative continuous semigroup operations on \(\mathbf {R}_+\) which are distributed by \(\star \) in terms of homeomorphism. As a consequence, we show that an arbitrary semigroup

    更新日期:2019-02-19
  • Precoherent quantale completions of partially ordered semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2019-01-19
    Bin Zhao, Changchun Xia

    Just as complete lattices can be viewed as the completions of posets, quantales can also be treated as the completions of partially ordered semigroups. Motivated by the study on the well-known Frink completions of posets, it is natural to consider the “Frink” completions for the case of partially ordered semigroups. For this purpose, we firstly introduce the notion of precoherent quantale completions

    更新日期:2019-01-19
  • On extensions of the generalized quadratic functions from “large” subsets of semigroups
    Semigroup Forum (IF 0.448) Pub Date : 2018-11-16
    A. Bahyrycz, J. Brzdęk, E. Jabłońska

    Let \((G,+)\) be a commutative semigroup, \(\tau \) be an endomorphism of G and involution, D be a nonempty subset of G, and \((H,+)\) be an abelian group, uniquely divisible by 2. Motivated by the extension problem of J. Aczél and the stability problem of S.M. Ulam, we show that if the set D is “sufficiently large”, then each function \(g{:} D\rightarrow H\) such that \(g(x+y)+g(x+\tau (y))=2g(x)+2g(y)\)

    更新日期:2018-11-16
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