• Semigroup Forum (IF 0.448) Pub Date : 2021-01-09
Muhtabar Muhtar, Abdukerim Haji, Mahsut Rozi, Abdulla Hoshur

By using the method of functional analysis, especially $$C_0$$-semigroup theory and spectral theory of linear operators we prove the well-posedness and the existence of a unique positive dynamic solution of a deteriorating system with multiple vacations of a repairman. Moreover, we show spectral properties of the system operator which imply that the system does not have a steady-state solution.

更新日期：2021-01-10
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-08
J. Koppitz, T. Musunthia

A fence is a particular partial order on a (finite) set, close to the linear order. In this paper, we calculate the rank of the semigroup $$\mathscr {FI}_{n}$$ of all order-preserving partial injections on an n-element fence. In particular, we provide a minimal generating set for $$\mathscr {FI}_{n}$$. In the present paper, n is odd since this problem for even n was already solved by I. Dimitrova and

更新日期：2021-01-10
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-07
Ülo Reimaa, Valdis Laan, Lauri Tart

Two semigroups are called Morita equivalent if the categories of firm right acts over them are equivalent. We prove that every semigroup is Morita equivalent to its subsemigroup consisting of all products of n factors. Using this we show that a finite semigroup is Morita equivalent to its largest factorisable subsemigroup. It follows that two finite semigroups are Morita equivalent if and only if their

更新日期：2021-01-08
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-07
V. D. Derech

A semigroup S is called a $$\varDelta$$-semigroup if the lattice of its congruences forms a chain relative to the inclusion. A local automorphism of a semigroup S is defined as an isomorphism between its two subsemigroups. The set of all local automorphisms of a semigroup S relative to the operation of composition forms an inverse monoid of local automorphisms. We present a classification of all finite

更新日期：2021-01-08
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-07
Fabián Arias, Jerson Borja

To a given numerical semigroup S we associate a family of subsemigroups $$\{\partial ^nS\}$$, $$n\in {\mathbb {N}}$$, that permits us to understand some of the structure of S. We characterize this family in case S is a supersymmetric numerical semigroup or S has maximal embedding dimension. We also prove some properties related to embedding dimension and certain symmetry of the minimal generating set

更新日期：2021-01-08
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-04

In a previous paper [1], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate free structures on the category of semihypergroups. We show that the natural free product structure along with the natural topology, although fails to give a free product for topological

更新日期：2021-01-05
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-04
Maedeh Soroushmehr

We study weak amenability of certain classes of commutative semigroup algebras. First, we present a class of commutative semigroups which semigroup algebras (like arbitrary group algebras) are always 2n-weakly amenable. Weak amenability of $$\ell ^1(S)$$ in terms of regular and irregular subsets of a commutative semigroup S is also studied.

更新日期：2021-01-05
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-04
Rodrigo Ponce, Mahamadi Warma

Let A be a densely defined closed, linear $$\omega$$-sectorial operator of angle $$\theta \in [0,\frac{\pi }{2})$$ on a Banach space X, for some $$\omega \in \mathbb {R}$$. We give an explicit representation (in terms of some special functions) and study the precise asymptotic behavior as time goes to infinity of solutions to the following diffusion equation with memory: $$\displaystyle u'(t)=Au(t)+(\kappa 更新日期：2021-01-05 • Semigroup Forum (IF 0.448) Pub Date : 2021-01-04 Hamid Sadeghi Nahrekhalaji Let S be a foundation topological semigroup and \(M_a(S)$$ the space of all measures $$\mu \in M(S)$$ for which the maps $$x\longmapsto |\mu |*\delta _{x}$$ and $$x\longmapsto \delta _{x}*|\mu |$$ from S into M(S) are weakly continuous. In the present paper, we introduce and study the concept of $$\phi$$-amenability for S and investigate the relations between $$\phi$$-amenability of S and essential

更新日期：2021-01-05
• Semigroup Forum (IF 0.448) Pub Date : 2021-01-04
Radu Păltănea, Mihaela Smuc

A quantitative estimate for the Trotter’s approximation theorem for the limiting semigroup of operators generated by the multidimensional Bernstein operators on a simplex is obtained. For this, an essential step consists in an explicit representation of the derivatives of higher order of multidimensional Bernstein operators.

更新日期：2021-01-05
• Semigroup Forum (IF 0.448) Pub Date : 2020-12-24
Yemon Choi, Mahya Ghandehari, Hung Le Pham

We continue the study of the AMNM property for weighted semilattices that was initiated in Choi (J Aust Math Soc 95(1):36–67, 2013. https://doi.org/10.1017/S1446788713000189). We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this “filter stability” property to hold. Examples

更新日期：2020-12-24
• Semigroup Forum (IF 0.448) Pub Date : 2020-12-10
Thomas Quinn-Gregson

A countable semigroup is $$\aleph _0$$-categorical if it can be characterised, up to isomorphism, by its first-order properties. In this paper we continue our investigation into the $$\aleph _0$$-categoricity of semigroups. Our main results are a complete classification of $$\aleph _0$$-categorical orthodox completely 0-simple semigroups, and descriptions of the $$\aleph _0$$-categorical members of

更新日期：2020-12-12
• Semigroup Forum (IF 0.448) Pub Date : 2020-12-01
Wha-Suck Lee, Christiaan Le Roux

We apply the recently introduced framework of admissible homomorphisms in the form of a convolution algebra of $$\mathbb{C}^2$$-valued admissible homomorphisms to handle two-dimensional uni-directional homogeneous stochastic kernels. The algebra product is a non-commutative extension of the Feller convolution needed for an adequate operator representation of such kernels: a pair of homogeneous transition

更新日期：2020-12-02
• Semigroup Forum (IF 0.448) Pub Date : 2020-11-16
Stuart Margolis

John Meakin has had a distinguished career of over half a century in the theory of semigroups. This article gives a synopsis of his most important contributions. The author, a long time collaborator, gives his personal memories of working with John and the influence he has had on his career.

更新日期：2020-11-17
• Semigroup Forum (IF 0.448) Pub Date : 2020-11-10
Fathi Hassine, Nadia Souayeh

We consider a coupled wave system with partial Kelvin–Voigt damping in the interval $$(-1,1)$$, where one wave is dissipative and the other is not. When the damping is effective in the whole domain $$(-1,1)$$, it was proven in Portillo Oquendo and Sànez Pacheco (Appl Math Lett 67:16–20, 2017) that the energy is a non-increasing function of the time variable, with a rate equals to $$t^{-\frac{1}{2}}$$

更新日期：2020-11-12
• Semigroup Forum (IF 0.448) Pub Date : 2020-10-27
Heydar Radjavi, Ahmed Ramzi Sourour

We investigate the structure of the multiplicative semigroup generated by the set of matrices that are unitarily equivalent to a given invertible matrix A. In particular, we give necessary and sufficient conditions for such a semigroup to be the special linear group or the general linear group or other classical matrix groups. Furthermore, we use the above to determine the subgroups of the general

更新日期：2020-10-30
• Semigroup Forum (IF 0.448) Pub Date : 2020-10-20
Balázs Kaprinai, Hajime Machida, Tamás Waldhauser

A binary operation f(x, y) is said to be lazy if every operation that can be obtained from f by composition is equivalent to f(x, y), f(x, x) or x. We describe lazy operations by identities (i.e., we determine all varieties of lazy groupoids), and we also characterize lazy groupoids up to isomorphism.

更新日期：2020-10-20
• Semigroup Forum (IF 0.448) Pub Date : 2020-10-20
Ru Liu, Sergey Piskarev

We consider the semidiscrete approximation of the Cauchy problem \begin{aligned} ({\mathbf {D}}_{t}^{\alpha }u)(t) = A u(t) +f\big (t,u(t)\big ), \quad t \in (0,T],\ u(0) = u^0,\ 0< \alpha <1, \end{aligned} on a Banach space, where the operator A generates an analytic and compact resolvent family $$\{S_{\alpha }(t,A)\}_{t\ge 0}$$ and the function $$f(\cdot , \cdot )$$ is strongly continuous. We

更新日期：2020-10-20
• 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
• 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
• 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
• 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
• 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
• Semigroup Forum (IF 0.448) Pub Date : 2020-09-30

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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
• 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
• 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
• 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
• 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
• Semigroup Forum (IF 0.448) Pub Date : 2020-06-16

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
• 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
• 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
• 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
• 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
• 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 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
• 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
• 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
• Semigroup Forum (IF 0.448) Pub Date : 2020-05-06

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
• 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
• 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 • 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
• 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
• 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
• 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
• 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
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