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Cartesian products of two CR sets 两个 CR 集的笛卡儿积
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-01 DOI: 10.1007/s00233-024-10449-3
Sayan Goswami
{"title":"Cartesian products of two CR sets","authors":"Sayan Goswami","doi":"10.1007/s00233-024-10449-3","DOIUrl":"https://doi.org/10.1007/s00233-024-10449-3","url":null,"abstract":"<p>The notions of a CR set is intimately related with the generalized van der Waerden’s theorem. We prove that the product of two CR sets is again a CR set. This answers Question 4.2 from Hindman et al. (Semigroup Forum 107:127–143, 2023).</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502597","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 certain semigroups of transformations whose restrictions belong to a given semigroup 关于限制属于给定半群的某些变换半群
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-01 DOI: 10.1007/s00233-024-10448-4
M. Sarkar, Shubh N. Singh
{"title":"On certain semigroups of transformations whose restrictions belong to a given semigroup","authors":"M. Sarkar, Shubh N. Singh","doi":"10.1007/s00233-024-10448-4","DOIUrl":"https://doi.org/10.1007/s00233-024-10448-4","url":null,"abstract":"<p>Let <i>T</i>(<i>X</i>) (resp. L(V)) be the semigroup of all transformations (resp. linear transformations) of a set <i>X</i> (resp. vector space <i>V</i>). For a subset <i>Y</i> of <i>X</i> and a subsemigroup <span>(mathbb {S}(Y))</span> of <i>T</i>(<i>Y</i>), consider the subsemigroup <span>(T_{mathbb {S}(Y)}(X) = {fin T(X):f_{upharpoonright _Y} in mathbb {S}(Y)})</span> of <i>T</i>(<i>X</i>), where <span>(f_{upharpoonright _Y}in T(Y))</span> agrees with <i>f</i> on <i>Y</i>. We give a new characterization for <span>(T_{mathbb {S}(Y)}(X))</span> to be a regular semigroup [inverse semigroup]. For a subspace <i>W</i> of <i>V</i> and a subsemigroup <span>(mathbb {S}(W))</span> of <i>L</i>(<i>W</i>), we define an analogous subsemigroup <span>(L_{mathbb {S}(W)}(V) = {fin L(V) :f_{upharpoonright _W} in mathbb {S}(W)})</span> of <i>L</i>(<i>V</i>). We describe regular elements in <span>(L_{mathbb {S}(W)}(V))</span> and determine when <span>(L_{mathbb {S}(W)}(V))</span> is a regular semigroup [inverse semigroup, completely regular semigroup]. If <span>(mathbb {S}(Y))</span> (resp. <span>(mathbb {S}(W))</span>) contains the identity of <i>T</i>(<i>Y</i>) (resp. <i>L</i>(<i>W</i>)), we describe unit-regular elements in <span>(T_{mathbb {S}(Y)}(X))</span> (resp. <span>(L_{mathbb {S}(W)}(V))</span>) and determine when <span>(T_{mathbb {S}(Y)}(X))</span> (resp. <span>(L_{mathbb {S}(W)}(V))</span>) is a unit-regular semigroup.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502596","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
Commutative nilpotent transformation semigroups 交换无势变换半群
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-07-01 DOI: 10.1007/s00233-024-10444-8
Alan J. Cain, António Malheiro, Tânia Paulista
{"title":"Commutative nilpotent transformation semigroups","authors":"Alan J. Cain, António Malheiro, Tânia Paulista","doi":"10.1007/s00233-024-10444-8","DOIUrl":"https://doi.org/10.1007/s00233-024-10444-8","url":null,"abstract":"<p>Cameron et al. determined the maximum size of a null subsemigroup of the full transformation semigroup <span>(mathcal {T}(X))</span> on a finite set <i>X</i> and provided a description of the null semigroups that achieve that size. In this paper we extend the results on null semigroups (which are commutative) to commutative nilpotent semigroups. Using a mixture of algebraic and combinatorial techniques, we show that, when <i>X</i> is finite, the maximum order of a commutative nilpotent subsemigroup of <span>(mathcal {T}(X))</span> is equal to the maximum order of a null subsemigroup of <span>(mathcal {T}(X))</span> and we prove that the largest commutative nilpotent subsemigroups of <span>(mathcal {T}(X))</span> are the null semigroups previously characterized by Cameron et al.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502595","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
Green’s relations on the variant semigroups of all transformations of a set that reflect an equivalence 反映等价性的集合所有变换的变异半群上的格林关系
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-27 DOI: 10.1007/s00233-024-10446-6
Lei Sun
{"title":"Green’s relations on the variant semigroups of all transformations of a set that reflect an equivalence","authors":"Lei Sun","doi":"10.1007/s00233-024-10446-6","DOIUrl":"https://doi.org/10.1007/s00233-024-10446-6","url":null,"abstract":"<p>Let <i>E</i> be an equivalence on a set <i>X</i> and let <span>(T_exists (X))</span> denote the semigroup (under composition) of all <span>(f:Xrightarrow X)</span> that reflect <i>E</i>. Fix an element <span>(theta in T_exists (X))</span> and for <span>(f,gin T_exists (X))</span>, define a new operation <span>(*)</span> on <span>(T_exists (X))</span> by <span>(f* g=ftheta g)</span> where <span>(ftheta g)</span> denotes the product of <span>(g,theta )</span> and <i>f</i> in the original sense. In this paper, we characterize Green’s relations on the variant semigroups <span>(T_exists (X,theta ))</span> of <span>(T_exists (X))</span> with sandwich operation <span>(theta )</span>.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502598","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
Semilattices of stratified extensions 分层扩展的半网格
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-24 DOI: 10.1007/s00233-024-10447-5
James Renshaw, William Warhurst
{"title":"Semilattices of stratified extensions","authors":"James Renshaw, William Warhurst","doi":"10.1007/s00233-024-10447-5","DOIUrl":"https://doi.org/10.1007/s00233-024-10447-5","url":null,"abstract":"<p>Grillet (Semigroup Forum 50:25–36, 1995) introduced the concept of stratified semigroups as a kind of generalisation of finite nilsemigroups. We extend Grillet’s ideas by introducing the notion of the base of a semigroup and show that a semigroup is stratified if and only if its base is either empty or consists of only the zero element. The general structure of semigroups with non-trivial bases is studied and we show that these can be described in terms of ideal extensions of semigroups by stratified semigroups. We consider certain types of group-bound semigroups and also ideal extensions of Clifford semigroups, and show how to describe them as semilattices of ideal extensions by stratified semigroups and provide a number of interesting examples.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502601","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 for coupled thermoelastic systems with nonlinear localized damping and Wentzell boundary conditions 具有非线性局部阻尼和温策尔边界条件的耦合热弹性系统的稳定性
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-18 DOI: 10.1007/s00233-024-10445-7
André Vicente
{"title":"Stability for coupled thermoelastic systems with nonlinear localized damping and Wentzell boundary conditions","authors":"André Vicente","doi":"10.1007/s00233-024-10445-7","DOIUrl":"https://doi.org/10.1007/s00233-024-10445-7","url":null,"abstract":"<p>This paper is concerning with the study of stability involving a thermoelastic system with internal nonlinear localized damping. The main novelty of the paper is to introduce to the study of thermoelastic system the general Wentzell boundary conditions associated to the internal heat equation. This boundary condition takes into account that there is a boundary source of heat which depends on the heat flow along the boundary, the heat flux across the boundary, and the temperature at the boundary. The tools are the use of multipliers with the construction of appropriate perturbed energy functionals.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502599","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
Some properties of monoids with infinity 有穷单子的一些性质
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-17 DOI: 10.1007/s00233-024-10443-9
Hamid Kulosman, Alica Miller
{"title":"Some properties of monoids with infinity","authors":"Hamid Kulosman, Alica Miller","doi":"10.1007/s00233-024-10443-9","DOIUrl":"https://doi.org/10.1007/s00233-024-10443-9","url":null,"abstract":"<p>We introduce the notion of PC cancellative additive monoids with infinity and use it to characterize cancellative additive principal ideal domains with infinity. Our characterization improves various known characterizations from the literature, both, in the context of the commutative cancellative monoids, as well as in the context of the analogues of the statements from the commutative ring theory.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502657","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
From plactic monoids to hypoplactic monoids 从广场一元体到低广场一元体
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-17 DOI: 10.1007/s00233-024-10436-8
Ricardo P. Guilherme
{"title":"From plactic monoids to hypoplactic monoids","authors":"Ricardo P. Guilherme","doi":"10.1007/s00233-024-10436-8","DOIUrl":"https://doi.org/10.1007/s00233-024-10436-8","url":null,"abstract":"<p>The plactic monoids can be obtained from the tensor product of crystals. Similarly, the hypoplactic monoids can be obtained from the quasi-tensor product of quasi-crystals. In this paper, we present a unified approach to these constructions by expressing them in the context of quasi-crystals. We provide a sufficient condition to obtain a quasi-crystal monoid for the quasi-tensor product from a quasi-crystal monoid for the tensor product. We also establish a sufficient condition for a hypoplactic monoid to be a quotient of the plactic monoid associated to the same seminormal quasi-crystal.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502600","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
Partial metrics and normed inverse semigroups 部分度量和规范化反半群
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-12 DOI: 10.1007/s00233-024-10442-w
Paul Poncet
{"title":"Partial metrics and normed inverse semigroups","authors":"Paul Poncet","doi":"10.1007/s00233-024-10442-w","DOIUrl":"https://doi.org/10.1007/s00233-024-10442-w","url":null,"abstract":"<p>Relying on the notions of submodular function and partial metric, we introduce normed inverse semigroups as a generalization of normed groups and sup-semilattices equipped with an upper valuation. We define the property of skew-convexity for a metric on an inverse semigroup, and prove that every norm on a Clifford semigroup gives rise to a right-subinvariant and skew-convex metric; it makes the semigroup into a Hausdorff topological inverse semigroup if the norm is cyclically permutable. Conversely, we show that every Clifford monoid equipped with a right-subinvariant and skew-convex metric admits a norm for which the metric topology and the norm topology coincide. We characterize convergence of nets and show that Cauchy completeness implies conditional monotone completeness with respect to the natural partial order of the inverse semigroup.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528742","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
Strongly Kreiss bounded operators in UMD Banach spaces UMD 巴拿赫空间中的强克赖斯有界算子
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-06-07 DOI: 10.1007/s00233-024-10441-x
Chenxi Deng, Emiel Lorist, Mark Veraar
{"title":"Strongly Kreiss bounded operators in UMD Banach spaces","authors":"Chenxi Deng, Emiel Lorist, Mark Veraar","doi":"10.1007/s00233-024-10441-x","DOIUrl":"https://doi.org/10.1007/s00233-024-10441-x","url":null,"abstract":"<p>In this paper we give growth estimates for <span>(Vert T^nVert )</span> for <span>(nrightarrow infty )</span> in the case <i>T</i> is a strongly Kreiss bounded operator on a <span>({{,textrm{UMD},}})</span> Banach space <i>X</i>. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and <span>(L^p)</span>-spaces, but also intermediate <span>({{,textrm{UMD},}})</span> spaces such as non-commutative <span>(L^p)</span>-spaces and variable Lebesgue spaces.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552713","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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