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Difference of Hilbert series of homogeneous monoid algebras and their normalizations Semigroup Forum (IF 0.7) Pub Date : 2024-03-11
Abstract Let Q be an affine monoid, \(\Bbbk [Q]\) the associated monoid \(\Bbbk \) -algebra, and \(\Bbbk [\overline{Q}]\) its normalization, where we let \(\Bbbk \) be a field. We discuss a difference of the Hilbert series of \(\Bbbk [Q]\) and \(\Bbbk [\overline{Q}]\) in the case where \(\Bbbk [Q]\) is homogeneous (i.e., standard graded). More precisely, we prove that if \(\Bbbk [Q]\) satisfies Serre’s
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Well-posedness of non-autonomous transport equation on metric graphs Semigroup Forum (IF 0.7) Pub Date : 2024-03-06 Christian Budde, Marjeta Kramar Fijavž
We consider transport processes on metric graphs with time-dependent velocities and show that, under continuity assumption of the velocity coefficients, the corresponding non-autonomous abstract Cauchy problem is well-posed by means of evolution families and evolution semigroups.
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Combinatorial results for semigroups of orientation-preserving and order-decreasing transformations Semigroup Forum (IF 0.7) Pub Date : 2024-02-23
Abstract Let \({{\mathscr {O}}{\mathscr {P}}{\mathscr {D}}}_{n}\) be the semigroup consisting of all orientation-preserving and order-decreasing full transformations on the finite chain \(X_{n}=\{1<\cdots
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Some nil-ai-semiring varieties Semigroup Forum (IF 0.7) Pub Date : 2024-02-14
Abstract We study some nil-ai-semiring varieties. We establish a model for the free object in the variety \(\textbf{FC}\) generated by all commutative flat semirings. Also, we provide two sufficient conditions under which a finite ai-semiring is nonfinitely based. As a consequence, we show that the power semiring \(P_{\scriptstyle {\dot{S}}_{c}(W)}\) of the finite nil-semigroup \({\dot{S}}_{c}(W)\)
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On atoms of the set of generalized numerical semigroups with fixed corner element Semigroup Forum (IF 0.7) Pub Date : 2024-02-14 Matheus Bernardini, Alonso S. Castellanos, Wanderson Tenório, Guilherme Tizziotti
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Quantitative estimates for bounded holomorphic semigroups Semigroup Forum (IF 0.7) Pub Date : 2024-02-12 Tuomas Hytönen, Stefanos Lappas
We revisit the theory of one-parameter semigroups of linear operators on Banach spaces in order to prove quantitative bounds for bounded holomorphic semigroups. Subsequently, relying on these bounds we obtain new quantitative versions of two recent results of Xu related to the vector-valued Littlewood–Paley–Stein theory for symmetric diffusion semigroups.
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Broken Möbius categories of $$Q_{3}$$ -type and their split inverse semigroups Semigroup Forum (IF 0.7) Pub Date : 2024-02-07 Emil Daniel Schwab
A class of Möbius monoids leads us to Möbius categories of \(Q_{3}\)-type via a particular breaking process, where \(Q_{3}\) is a quiver with three arrows (atoms). In this paper we show that a quasi-commutativity regarding composable atoms uniquely determines (via a certain local congruence) a half-factorial broken Möbius category of \(Q_{3}\)-type as a quotient category of the path category of \(Q_{3}\)
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Non-K3 Weierstrass numerical semigroups Semigroup Forum (IF 0.7) Pub Date : 2024-02-07 Jiryo Komeda, Makiko Mase
We generalize the result of Reid (J Lond Math Soc 13:454–458, 1976), namely, we prove that a curve of genus \(\geqq g^2+4g+6\) having a double cover of a hyperelliptic curve of genus \(g\geqq 2\) does not lie as a non-singular curve on any K3 surface. Applying this result we construct non-K3 Weierstrass numerical semigroups. A numerical semigroup H is said to be Weierstrass if there exists a pointed
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Orderability of the prefix expansion of an ordered inverse semigroup Semigroup Forum (IF 0.7) Pub Date : 2024-02-02 G. H. Esslamzadeh, M. A. Faraji, B. Tabatabaie Shourijeh
We answer two orderability questions about the prefix expansion semigroup Pr(G) of an inverse semigroup G. We show that if G is a left ordered inverse semigroup, then Pr(G) is a left ordered inverse semigroup if and only if it is an ordered inverse semigroup, if and only if G is a semilattice. We also prove that when G and Pr(G) are left ordered, Pr(G) is proper if and only if G is proper. Positivity
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Semigroup collaborations between elementary operations Semigroup Forum (IF 0.7) Pub Date : 2024-02-02 Sergio R. López-Permouth, Aaron Nicely, Majed Zailaee
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The Frobenius problem over number fields with a real embedding Semigroup Forum (IF 0.7) Pub Date : 2024-01-29 Alex Feiner, Zion Hefty
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Affine semigroups of maximal projective dimension-II Semigroup Forum (IF 0.7) Pub Date : 2024-01-24 Om Prakash Bhardwaj, Indranath Sengupta
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Completions of posemigroups by cuts and beyond Semigroup Forum (IF 0.7) Pub Date : 2023-12-19 Shuang Li, Xia Zhang
This work is devoted to describing the completion of a posemigroup by cuts. We introduce cut-stable morphisms between posemigroups and obtain that the category \({\mathsf {RQuant_{\wedge }}}\) of quantales with meet and residuals preserving morphisms is a full reflective subcategory of the category \({\textsf{CSPoSgr}}\) of posemigroups with cut-stable morphisms. As an application, we also characterize
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Moment functions of higher rank on some types of hypergroups Semigroup Forum (IF 0.7) Pub Date : 2023-12-11 Żywilla Fechner, Eszter Gselmann, László Székelyhidi
We consider moment functions of higher order. In our earlier paper, we have already investigated the moment functions of higher order on groups. The main purpose of this work is to prove characterization theorems for moment functions on the multivariate polynomial hypergroups and on the Sturm–Liouville hypergroups. In the first case, the moment generating functions of higher rank are partial derivatives
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Limit varieties generated by finite non-J-trivial aperiodic monoids Semigroup Forum (IF 0.7) Pub Date : 2023-12-04 Olga B. Sapir
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Joint continuity in semitopological monoids and semilattices Semigroup Forum (IF 0.7) Pub Date : 2023-12-04 Alexander V. Osipov, Konstantin Kazachenko
We study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson’s results to some class of pseudocompact spaces. Also, we introduce the concept of a weak \(q_D\)-space and prove that a pseudocompact space and a weak \(q_D\)-space form a Grothendieck pair. As an application of the main result, we investigate the continuity
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Homeomorphism groups on the positive real numbers defined by binary operations Semigroup Forum (IF 0.7) Pub Date : 2023-11-08 Sin-Ei Takahasi
Given a continuous binary operation \(\star \) on the positive real numbers \({\textbf{R}}_+\) with ordinary topology, we consider the homeomorphism group \(Homeo_{\star }({\textbf{R}}_+)\) consisting of all homeomorphisms on \({\textbf{R}}_+\) which preserve \(\star \). We show that if \(\star \) is any continuous cancellative semigroup operation on \({\textbf{R}}_+\), then \(Homeo_{\star }({\textbf{R}}_+)\)
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Formations of orthodox semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-11-08 Gracinda M. S. Gomes, Ana-Catarina C. Monteiro
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On the structure of semigroups whose regular elements are completely regular Semigroup Forum (IF 0.7) Pub Date : 2023-11-08 Xavier Mary
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Equationally defined classes of semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-11-03 Peter M. Higgins, Marcel Jackson
We apply, in the context of semigroups, the main theorem from the authors’ paper “Algebras defined by equations” (Higgins and Jackson in J Algebra 555:131–156, 2020) that an elementary class \({\mathscr {C}}\) of algebras which is closed under the taking of direct products and homomorphic images is defined by systems of equations. We prove a dual to the Birkhoff theorem in that if the class is also
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Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set Semigroup Forum (IF 0.7) Pub Date : 2023-10-31 Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro
We consider the inverse submonoids \(\mathcal {OPDI}_n\), \(\mathcal {MDI}_n\) and \(\mathcal {ODI}_n\) of the dihedral inverse monoid \(\mathcal{D}\mathcal{I}_n\) of all orientation-preserving, monotone and order-preserving transformations, respectively. Our goal is to exhibit presentations for each of these three monoids.
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An extension to “A subsemigroup of the rook monoid” Semigroup Forum (IF 0.7) Pub Date : 2023-10-19 George Fikioris, Giannis Fikioris
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The local bisection hypothesis for twisted groupoid C*-algebras Semigroup Forum (IF 0.7) Pub Date : 2023-10-17 Becky Armstrong, Jonathan H. Brown, Lisa Orloff Clark, Kristin Courtney, Ying-Fen Lin, Kathryn McCormick, Jacqui Ramagge
In this note, we present criteria that are equivalent to a locally compact Hausdorff groupoid G being effective. One of these conditions is that G satisfies the C*-algebraic local bisection hypothesis; that is, that every normaliser in the reduced twisted groupoid C*-algebra is supported on an open bisection. The semigroup of normalisers plays a fundamental role in our proof, as does the semigroup
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Representations and identities of Baxter monoids with involution Semigroup Forum (IF 0.7) Pub Date : 2023-10-12 Bin Bin Han, Wen Ting Zhang, Yan Feng Luo, Jin Xing Zhao
Let \((\textsf{baxt}_n,^\sharp )\) be the Baxter monoid of finite rank n with Schützenberger’s involution \(^{\sharp }\). In this paper, it is shown that \((\textsf{baxt}_n,^\sharp )\) admits a faithful representation by an involution monoid of upper triangular matrices over any semiring from a large class including the tropical semiring under the skew transposition. Then a transparent combinatorial
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Regular semigroups weakly generated by one element Semigroup Forum (IF 0.7) Pub Date : 2023-10-11 Luís Oliveira
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A new generation criterion theorem for $$C_0$$ -semigroups implying a generalization of Kaiser–Weis–Batty’s perturbation theorem Semigroup Forum (IF 0.7) Pub Date : 2023-10-10 Hatem Megdiche
By proving existence, regularity and uniqueness of solutions to Cauchy problems governed by abstract unbounded operators with finite pseudo-spectral bounds as an alternative and a serious enhancement of results by Melnikova and Filinkov, we establish a new generation criterion theorem for \(C_0\)-semigroups in general Banach spaces. A generalization of Kaiser–Weis–Batty’s perturbation generation theorem
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The Frobenius problem for numerical semigroups generated by sequences of the form $$ca^n-d$$ Semigroup Forum (IF 0.7) Pub Date : 2023-10-02 Fabián Arias, Jerson Borja, Calixto Rhenals
For a positive integer n, consider the submonoid \(S_n\) of \({\mathbb {N}}\) generated by the sequence of positive integers \({\textbf{s}}_j=ca^{n+j}-d\), \(j\in {\mathbb {N}}\), where a, c, and d are integers, \(a\ge 2\), and c is positive. We unify ideas and results from previous works on specific cases for a, c, and d, and we prove some conjectures that arise in the general case. Under fairly general
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On the atomic structure of torsion-free monoids Semigroup Forum (IF 0.7) Pub Date : 2023-10-03 Felix Gotti, Joseph Vulakh
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Normal subsemigroups of finite transformation semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-09-25 Janusz Konieczny
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The quantale of order-preserving maps of a completely distributive lattice Semigroup Forum (IF 0.7) Pub Date : 2023-09-25 Hongwei Wu
Simple quantales were introduced by Paseka and are closely related to \(C^{*}\)-algebras. The sublattice \({\mathcal {S}}(L)\) of \(L^{L}\) is a prototypical example of a simple quantale under the multiplication defined by composition \(\circ \), where \({\mathcal {S}}(L)\) denotes the set of sup-preserving endomaps of a nontrivial complete lattice L and \(L^{L}\) denotes the set of order-preserving
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Ehresmann–Schein–Nambooripad theorems for classes of biunary semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-09-20 Tim Stokes
We obtain an ESN theorem for a very general class of biunary semigroups with idempotent-valued domain and range operations, representing them in terms of small categories equipped with a suitable biaction of the identities on the category. Our results generalise the recent work of Fitzgerald and Kinyon connecting localisable semigroups to transcription categories, as well as that of Lawson linking
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Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes Semigroup Forum (IF 0.7) Pub Date : 2023-09-20 Miroslav Ćirić, Jelena Ignjatović, Predrag Stanimirović
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Levi-Civita functional equations on commutative monoids with tractable prime ideals Semigroup Forum (IF 0.7) Pub Date : 2023-09-13 Bruce Ebanks
Under suitable conditions on the unknown functions, solutions of Levi-Civita functional equations on commutative monoids with no prime ideals are exponential polynomials. This is not generally the case on commutative monoids with prime ideals. Here we describe the solutions of Levi-Civita equations on commutative monoids in which every prime ideal is tractable. Monoids with this property include those
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Variational principle for BS-dimension of subsets of finitely generated free semigroup actions Semigroup Forum (IF 0.7) Pub Date : 2023-08-30 Xin Liu, Zhumin Ding
We consider a topological dynamical system under the action of a finitely generated free semigroup. Using the Carathéodory structure, we define BS-dimension on an arbitrary subset and obtain a Bowen’s equation which illustrates the relation of BS-dimension to Pesin–Pitskel topological pressure defined in Zhong and Chen (Acta Math Sinica Engl Ser 37(9):1401–1414, 2021). Then, an analogue of Billingsley’s
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On factorization systems for S-acts Semigroup Forum (IF 0.7) Pub Date : 2023-08-30 Huanyun Li, Rongmin Zhu
The concept of a weak factorization system for modules has found an application in one of the proofs of the celebrated flat cover conjecture for modules over a ring. We examine this notion in the context of S-acts over a monoid S. Bailey and Renshaw constructed a weak factorization system related to the existence of precovers of S-acts and showed that the class of flat right S-acts satisfies a related
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Semilattices of simple and regular n-ary semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-08-22 Jukkrit Daengsaen, Sorasak Leeratanavalee
The semilattice congruence \(\mathscr {N}\), which identifies two elements if they generate the same principal filter, plays a significant role in studying the decomposition of semigroups. We investigate the remarkable properties of the semilattice congruence \(\mathscr {N}\) on n-ary semigroups, where \(n\ge 3\), and use these properties to describe the structure of n-ary semigroups which are decomposable
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Analysis and control of integro-differential Volterra equations with delays Semigroup Forum (IF 0.7) Pub Date : 2023-08-21 Youness El Kadiri, Said Hadd, Hamid Bounit
We present a novel approach to address integro-differential systems incorporating state, input, and output delays. Our approach leverages product spaces and employs a boundary perturbation technique. Initially, we focus on state-delay equations, wherein we introduce a variation of constants formula for the mild solution. Additionally, we establish spectral properties using a characteristic equation
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Quasi-polynomial growth of numerical and affine semigroups with constrained gaps Semigroup Forum (IF 0.7) Pub Date : 2023-08-10 Michael DiPasquale, Bryan R. Gillespie, Chris Peterson
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Biunit pairs in semiheaps and associated semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-08-09 Bernard Rybołowicz, Carlos Zapata-Carratalá
The notion of neutral element generalizes to a pair of elements in ternary algebras. Biunit pairs are introduced as pairs of elements in a semiheap that generalize the notion of Mal’cev element. In order to generalize the known correspondences between semiheaps and certain kinds of semigroups, families of functions generalizing involutions and conjugations, called switches and warps, are investigated
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Scalable monoids and quantity calculus Semigroup Forum (IF 0.7) Pub Date : 2023-08-02 Dan Jonsson
We define scalable monoids and prove their fundamental properties. Congruence relations on scalable monoids, direct and tensor products, subalgebras and homomorphic images of scalable monoids, and unit elements of scalable monoids are defined and investigated. A quantity space is defined as a commutative scalable monoid over a field, admitting a finite basis similar to a basis for a free abelian group
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Weakly invariant fuzzy quasi-pseudometrics on semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-08-01 Pi-Yu Li, Jie Liu, Jian-Cai Wei, Li-Hong Xie
We obtain conditions on fuzzy quasi-pseudometrics on either semigroups or groups which imply that they are either fuzzy topological semigroups or topological groups. Our main results are: (1) Let \((S, M, *)\) be a fuzzy quasi-pseudometric right topological semigroup (resp., group) such that \((M, *)\) is left weakly invariant; then \((S, M, *)\) is a fuzzy quasi-pseudometric topological semigroup
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Pettis-integration approach for characterizing almost periodic functions and flows Semigroup Forum (IF 0.7) Pub Date : 2023-08-01 Fardin Amini, Shahram Saeidi
In this paper, we investigate properties, characterizations and compactifications of almost periodic functions with values in a topological vector space. The techniques applied are based essentially on an analogue of a representation in Pettis-integration. Applications of the results to flows are indicated.
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Growth bounds for $$\alpha $$ -times resolvent families Semigroup Forum (IF 0.7) Pub Date : 2023-08-01 Seyedeh Marzieh Ghavidel, Mina Shahali
In this paper, we consider \(\alpha \)-times resolvent families that are bounded by a given function \({ \varphi }\). We present Hille–Yosida type conditions for an operator to be the generator of a \({ \varphi }\)-bounded \(\alpha \)-times resolvent family. Next, we find some integral estimates on the resolvent of an operator that are sufficient to generate an \(\alpha \)-times resolvent family. We
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Combinatorially rich sets in arbitrary semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-07-25 Neil Hindman, Hedie Hosseini, Dona Strauss, M. A. Tootkaboni
Combinatorially rich sets were introduced by Bergelson and Glasscock (J Comb Theory Ser A 172:105203, 2020) for commutative semigroups and shown to have several properties justifying their name. We extend the definition to arbitrary semigroups and establish the relationships of combinatorially rich sets to other notions of largeness in semigroups.
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Fibration mappings of topological left almost semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-07-25 Ljubiša D. R. Kočinac, Hakeem A. Othman
We discuss the notion of fibration property of continuous functions in the theory of topological left almost semigroups. The concept of L-fibration is introduced and investigated. The restriction and composition properties of L-fibrations and the lifting property of L-fibrations are studied through the concepts of L-lifting function and L-regular lifting function. The study shows the uniqueness of
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Tropical linear representations of the Chinese monoid Semigroup Forum (IF 0.7) Pub Date : 2023-06-19 Zur Izhakian, Glenn Merlet
We introduce a faithful tropical linear representation of the Chinese monoid, and thus prove that this monoid admits all the semigroup identities satisfied by upper triangular tropical matrices.
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On gonality and canonical models of unicuspidal rational curves Semigroup Forum (IF 0.7) Pub Date : 2023-06-15 Naamã Galdino, Renato Vidal Martins, Danielle Nicolau
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On the solvability of fourth-order boundary value problems with accretive operators Semigroup Forum (IF 0.7) Pub Date : 2023-06-13 Mohammed Benharrat, Fairouz Bouchelaghem, Alexandre Thorel
We consider an abstract fourth order boundary value problem where the coefficients are accretive operators in Hilbert space. We show existence, uniqueness and maximal regularity of the solution under some necessary and sufficient conditions on the data. To this end, we give an explicit representation formula, using analytic semigroups, sectorial operators with Bounded Imaginary Powers, the theory of
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Arithmetic of additively reduced monoid semidomains Semigroup Forum (IF 0.7) Pub Date : 2023-06-12 Scott T. Chapman, Harold Polo
The term semidomain refers to a subset S of an integral domain R, in which the pairs \((S,+)\) and \((S, \cdot )\) are semigroups with identities. If S contains no additive inverses except 0, we say that S is additively reduced. By taking polynomial expressions with coefficients in S and exponents in a torsion-free monoid M, we obtain the additively reduced monoid semidomain S[M]. In this paper, we
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Globalization of partial actions of semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-06-13 Ganna Kudryavtseva, Valdis Laan
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Decidability of CPC-irreducibility of subshifts of finite type over free groups Semigroup Forum (IF 0.7) Pub Date : 2023-05-30 Jung-Chao Ban, Chih-Hung Chang, Yu-Liang Wu
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The monoid of all orientation-preserving and extensive partial transformations on a finite chain Semigroup Forum (IF 0.7) Pub Date : 2023-05-30 Ping Zhao, Huabi Hu
Let \(\mathcal {POPE}_n\) be the monoid of all orientation-preserving and extensive partial transformations on \({\textbf {n}}=\{1,\dots , n\}\). In this paper, we characterize the structure of the generating sets of \(\mathcal {POPE}_n\), and prove that each generating set of \(\mathcal {POPE}_n\) contains a minimal idempotent generating set of \(\mathcal {POPE}_n\). Moreover, the minimal generating
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Zigzag structures in IP* sets Semigroup Forum (IF 0.7) Pub Date : 2023-05-25 Teng Zhang
Goswami asked whether, if A is an IP* set in \(({\mathbb {N}},+)\) and an l-sequence in \({\mathbb {N}}\) is given, it must have a sum subsystem all of whose zigzag finite sums and products are in A. He gave an affirmative answer if A is a dynamical IP* set. Debnath and Goswami got a stronger result for dynamical IP* sets in weak rings, where the zigzag finite products are in any order. In this paper
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Characterization of Orlicz admissibility Semigroup Forum (IF 0.7) Pub Date : 2023-05-23 René Hosfeld, Birgit Jacob, Felix Schwenninger
We extend two characterizations of admissible operators with respect to \(\textrm{L}^p\) to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly continuous semigroup and in terms of a resolvent estimate.
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Unit-regular and semi-balanced elements in various semigroups of transformations Semigroup Forum (IF 0.7) Pub Date : 2023-05-22 Mosarof Sarkar, Shubh N. Singh
Let T(X) be the full transformation semigroup on a set X, and let L(V) be the semigroup under composition of all linear transformations on a vector space V over a field. For a subset Y of X and a subspace W of V, consider the semigroups \({\overline{T}}(X, Y) = \{f\in T(X):Yf \subseteq Y\}\) and \({\overline{L}}(V, W) = \{f\in L(V):Wf \subseteq W\}\) under composition. We describe unit-regular elements
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Laws for generalised interior operations in semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-05-18 Tim Stokes
Motivated by interior operators and by analogous generalisations of closure operators to semigroups in general, we define left, right and two-sided interior operations on a semigroup S in terms of a distinguished set of idempotents E using the natural order. In the left-sided case, we require that for all \(s\in S\), there is a largest \(e\in E\) under the natural order such that \(es=e\). We generalise
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Variational principles for topological invariance entropy of semigroup actions Semigroup Forum (IF 0.7) Pub Date : 2023-05-17 Zhumin Ding
We introduce three types of topological invariance entropies with respect to admissible partitions for semigroup actions with a regular system and give the relationship between them. We also define two types of measure-theoretic invariance entropies for the above semigroup actions and show that the two measure-theoretic invariance entropies are invariant under measure conjugacies. Last, we illustrate
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A remark on contracting inverse semigroups Semigroup Forum (IF 0.7) Pub Date : 2023-05-16 Giuliano Boava, Ruy Exel
A semi-lattice is said to be tree-like when any two of its elements are either orthogonal or comparable. Given an inverse semigroup \(\mathcal{S}\) whose idempotent semi-lattice is tree-like, and such that all tight filters are ultra-filters, we present a necessary and sufficient condition for \(\mathcal{S}\) to be contracting which looks closer in spirit to the notion of contracting actions than a
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A semigroup defining the Gröbner degeneration of a toric ideal Semigroup Forum (IF 0.7) Pub Date : 2023-05-08 Hernán de Alba Casillas, Daniel Duarte, Raúl Vargas Antuna
We give an explicit set of generators for the semigroup of the Gröbner degeneration of a toric ideal. This set of generators is used to study algebraic properties of the semigroup it generates: approximation of semigroups, non-preservation of saturation, Betti elements, uniqueness of presentations, and Möbius functions.
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Torsion factors of commutative monoid semirings Semigroup Forum (IF 0.7) Pub Date : 2023-05-02 Miroslav Korbelář
Let P be a finitely generated commutative semiring with a unity. It was shown recently that if the multiplicative reduct of P is a group then P is additively idempotent. We extend this result by showing that P is additively idempotent, provided that P is additively divisible. We further generalize this result using a weaker form of divisibility (almost-divisibility) as follows. Let S be a semiring