• 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 : 2020-03-11 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 : 2020-02-25
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
• 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
• 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
• Semigroup Forum (IF 0.448) Pub Date : 2020-02-07

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Semigroup Forum (IF 0.448) Pub Date : 2019-09-28

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Semigroup Forum (IF 0.448) Pub Date : 2019-05-28

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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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