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A cluster algebra approach to presentations of the monoid of uniform block permutations 用聚类代数的方法来呈现统一块排列的单项式
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-29 DOI: 10.1007/s00233-024-10457-3
Bing Duan, Jian-Rong Li, Yan-Feng Luo
{"title":"A cluster algebra approach to presentations of the monoid of uniform block permutations","authors":"Bing Duan, Jian-Rong Li, Yan-Feng Luo","doi":"10.1007/s00233-024-10457-3","DOIUrl":"https://doi.org/10.1007/s00233-024-10457-3","url":null,"abstract":"<p>We describe the mutation class of a certain quiver with a frozen vertex and associate these quivers with potentials appearing in our mutation class to presentations of the monoid <span>({mathscr {P}}_{n+1})</span> of uniform block permutations on the set <span>({1,2,ldots , n+1})</span>. Some classical and known presentations of <span>({mathscr {P}}_{n+1})</span>, including FitzGerald’s presentation and Everitt and Fountain’s presentation, are recovered.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of coupled wave equations with variable coefficients, localised Kelvin–Voigt damping and time delay 具有可变系数、局部开尔文-沃伊特阻尼和时间延迟的耦合波方程的稳定性
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-26 DOI: 10.1007/s00233-024-10453-7
Houssem Herbadji, Ammar Khemmoudj
{"title":"Stability of coupled wave equations with variable coefficients, localised Kelvin–Voigt damping and time delay","authors":"Houssem Herbadji, Ammar Khemmoudj","doi":"10.1007/s00233-024-10453-7","DOIUrl":"https://doi.org/10.1007/s00233-024-10453-7","url":null,"abstract":"<p>We consider the stabilization of two weakly dissipative wave equations with variable coefficients, localized Kelvin–Voigt damping, mixed boundary condition and time delay. The well posedness is obtained by the semigroup method. Using a unique continuation result, we show that the system is strongly stable. Then, we show that the system is not exponentially stable. Finally, using a frequency domain approach combined with multiplier method, we establish a polynomial energy decay rate for the undelayed system. Then, we prove that the system with delay has the same decay rate.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A defining equation and reflective subcategories of quasicontinuous complete semilattices 准连续完整半网格的定义方程和反射子类
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-26 DOI: 10.1007/s00233-024-10459-1
Wei Luan, Qingguo Li
{"title":"A defining equation and reflective subcategories of quasicontinuous complete semilattices","authors":"Wei Luan, Qingguo Li","doi":"10.1007/s00233-024-10459-1","DOIUrl":"https://doi.org/10.1007/s00233-024-10459-1","url":null,"abstract":"<p>In 1981, Gerhard Gierz and Jimmie Lawson gave a necessary condition for a complete lattice to be quasicontinuous using an equation. However, whether quasicontinuous lattices can be characterized by equations has remained unknown. In this paper, we give an equational characterization of quasicontinuous complete semilattices. Furthermore, we investigate congruences of quasicontinuous complete semilattices. We derive the first isomorphism theorem for quasicontinuous complete semilattices in the context of C-congruences. As a consequence, we show that the category of all continuous complete semilattices with maps preserving directed sups and nonempty infs is a reflective full subcategory of quasicontinuous complete semilattices.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lattices of varieties of plactic-like monoids 类方格一元组品种的网格
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-24 DOI: 10.1007/s00233-024-10435-9
Thomas Aird, Duarte Ribeiro
{"title":"Lattices of varieties of plactic-like monoids","authors":"Thomas Aird, Duarte Ribeiro","doi":"10.1007/s00233-024-10435-9","DOIUrl":"https://doi.org/10.1007/s00233-024-10435-9","url":null,"abstract":"<p>We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the axiomatic ranks of their elements, obtain plactic-like congruences whose corresponding factor monoids generate varieties in the lattice, and determine which varieties are joins of the variety of commutative monoids and a finitely generated variety. We also show that the hyposylvester and metasylvester monoids generate the same variety as the sylvester monoid.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the equivalence between the uniform exponential stability of a $$C_0$$ -semigroup and the boundedness of the resolvent 论$$C_0$$-半群的均匀指数稳定性与解析量的有界性之间的等价性
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-24 DOI: 10.1007/s00233-024-10455-5
Abdelhadi El Harfi
{"title":"On the equivalence between the uniform exponential stability of a $$C_0$$ -semigroup and the boundedness of the resolvent","authors":"Abdelhadi El Harfi","doi":"10.1007/s00233-024-10455-5","DOIUrl":"https://doi.org/10.1007/s00233-024-10455-5","url":null,"abstract":"<p>We consider a <span>(C_0)</span>-semigroup on a Banach space such that the resolvent is uniformly bounded on the right half-plane. In this paper we provide a condition on the resolvent which is sufficient and necessary for the uniform exponential stability of such a semigroup. As a consequence, we give an alternative proof of Gearhart’s theorem (Trans. Amer. Math. Soc. <b> 236</b>, 385–394 (1978)). The approach lies on a complex inversion formula and tempered distributions.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Preface of the special issue dedicated to selected semigroup papers from the Conference on Theoretical and Computational Algebra 2023 2023 年理论与计算代数会议半群论文特刊序言
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-24 DOI: 10.1007/s00233-024-10454-6
João Araújo, Alan J. Cain, António Malheiro, Mikhail Volkov
{"title":"Preface of the special issue dedicated to selected semigroup papers from the Conference on Theoretical and Computational Algebra 2023","authors":"João Araújo, Alan J. Cain, António Malheiro, Mikhail Volkov","doi":"10.1007/s00233-024-10454-6","DOIUrl":"https://doi.org/10.1007/s00233-024-10454-6","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141809210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thick sets are exactly the sets with Følner density 1 厚集正是福尔纳密度为 1 的集合
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-22 DOI: 10.1007/s00233-024-10456-4
Neil Hindman, Dona Strauss
{"title":"Thick sets are exactly the sets with Følner density 1","authors":"Neil Hindman, Dona Strauss","doi":"10.1007/s00233-024-10456-4","DOIUrl":"https://doi.org/10.1007/s00233-024-10456-4","url":null,"abstract":"<p><i>Følner density</i> is a very natural notion of density which is defined on any semigroup satisfying the Strong Følner Condition (SFC). (These include all commutative semigroups and all left cancellative left amenable semigroups.) <i>Piecewise syndetic</i> and <i>thick</i> are notions of largeness arising from topological dynamics. It has been known that if <i>S</i> satisfies SFC and is either left cancellative or satisfies a weak right cancellation requirement, then every thick subset has density 1. We show here that in any semigroup <i>S</i> satisfying SFC a subset of <i>S</i> is thick if and only if it has density 1. As a consequence, every piecewise syndetic set has positive density.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finitely and non-finitely related words 有穷关联词和无穷关联词
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-19 DOI: 10.1007/s00233-024-10452-8
Daniel Glasson
{"title":"Finitely and non-finitely related words","authors":"Daniel Glasson","doi":"10.1007/s00233-024-10452-8","DOIUrl":"https://doi.org/10.1007/s00233-024-10452-8","url":null,"abstract":"<p>An algebra is finitely related (or has finite degree) if its term functions are determined by some finite set of finitary relations. Nilpotent monoids built from words, via Rees quotients of free monoids, have been used to exhibit many interesting properties with respect to the finite basis problem. We show that much of this intriguing behaviour extends to the world of finite relatedness by using interlocking patterns called chain, crown, and maelstrom words. In particular, we show that there are large classes of non-finitely related nilpotent monoids that can be used to construct examples of: ascending chains of varieties alternating between finitely and non-finitely related; non-finitely related semigroups whose direct product are finitely related; the addition of an identity element to a non-finitely related semigroup to produce a finitely related semigroup.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalizations of free monoids 自由单体的广义
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-12 DOI: 10.1007/s00233-024-10450-w
Mark V. Lawson, Alina Vdovina
{"title":"Generalizations of free monoids","authors":"Mark V. Lawson, Alina Vdovina","doi":"10.1007/s00233-024-10450-w","DOIUrl":"https://doi.org/10.1007/s00233-024-10450-w","url":null,"abstract":"<p>We generalize free monoids by defining <i>k</i>-monoids. These are nothing other than the one-vertex higher-rank graphs used in <span>(C^{*})</span>-algebra theory with the cardinality requirement waived. The 1-monoids are precisely the free monoids. We then take the next step and generalize <i>k</i>-monoids in such a way that self-similar group actions yield monoids of this type.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Identities of Hecke–Kiselman monoids 赫克-基塞尔曼单体的同一性
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-08 DOI: 10.1007/s00233-024-10451-9
Magdalena Wiertel
{"title":"Identities of Hecke–Kiselman monoids","authors":"Magdalena Wiertel","doi":"10.1007/s00233-024-10451-9","DOIUrl":"https://doi.org/10.1007/s00233-024-10451-9","url":null,"abstract":"<p>It is shown that the Hecke–Kiselman monoid <span>({text {HK}}_{Theta })</span> associated to a finite oriented graph <span>(Theta )</span> satisfies a semigroup identity if and only if <span>({text {HK}}_{Theta })</span> does not have free noncommutative subsemigroups. It follows that this happens exactly when the semigroup algebra <span>(K[{text {HK}}_{Theta }])</span> over a field <i>K</i> satisfies a polynomial identity. The latter is equivalent to a condition expressed in terms of the graph <span>(Theta )</span>. The proof allows to derive concrete identities satisfied by such monoids <span>({text {HK}}_{Theta })</span>.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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