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The additively idempotent semiring $$S_7^0$$ is nonfinitely based 可加可幂等分线$$S_7^0$$是非无限基于的
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-03-20 DOI: 10.1007/s00233-024-10420-2
Yanan Wu, Miaomiao Ren, Xianzhong Zhao
{"title":"The additively idempotent semiring $$S_7^0$$ is nonfinitely based","authors":"Yanan Wu, Miaomiao Ren, Xianzhong Zhao","doi":"10.1007/s00233-024-10420-2","DOIUrl":"https://doi.org/10.1007/s00233-024-10420-2","url":null,"abstract":"<p>We show that the additively idempotent semiring <span>(S_7^0)</span> has no finite basis for its equational theory. This answers an open problem posed by Jackson et al. (J Algebra 611:211–245, 2022).</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197254","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 splittings and integration of almost periodic functions with and without geometry 关于有几何和无几何的几乎周期函数的分裂和积分
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-03-19 DOI: 10.1007/s00233-024-10415-z
Christian Budde, Josef Kreulich
{"title":"On splittings and integration of almost periodic functions with and without geometry","authors":"Christian Budde, Josef Kreulich","doi":"10.1007/s00233-024-10415-z","DOIUrl":"https://doi.org/10.1007/s00233-024-10415-z","url":null,"abstract":"<p>Recently, the authors introduced the notion of weighted semigroups which apply to sun-dual semigroups and especially to the translation semigroup on the space of left continuous functions with values in dual spaces. In this article, we will show that it is sufficient that we either assume geometry on the Banach, or an abelian structure on the minimal subgroup to prove almost periodicity. This yields a different approach to the almost periodicity of semigroups and integrals, by extending Basit generalized Kadets result to general groups, to obtain almost periodicity.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165511","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
Difference of Hilbert series of homogeneous monoid algebras and their normalizations 同质单元代数的希尔伯特级数差及其归一化
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-03-11 DOI: 10.1007/s00233-024-10414-0
{"title":"Difference of Hilbert series of homogeneous monoid algebras and their normalizations","authors":"","doi":"10.1007/s00233-024-10414-0","DOIUrl":"https://doi.org/10.1007/s00233-024-10414-0","url":null,"abstract":"<h3>Abstract</h3> <p>Let <em>Q</em> be an affine monoid, <span> <span>(Bbbk [Q])</span> </span> the associated monoid <span> <span>(Bbbk )</span> </span>-algebra, and <span> <span>(Bbbk [overline{Q}])</span> </span> its normalization, where we let <span> <span>(Bbbk )</span> </span> be a field. We discuss a difference of the Hilbert series of <span> <span>(Bbbk [Q])</span> </span> and <span> <span>(Bbbk [overline{Q}])</span> </span> in the case where <span> <span>(Bbbk [Q])</span> </span> is homogeneous (i.e., standard graded). More precisely, we prove that if <span> <span>(Bbbk [Q])</span> </span> satisfies Serre’s condition <span> <span>((S_2))</span> </span>, then the degree of the <em>h</em>-polynomial of <span> <span>(Bbbk [Q])</span> </span> is always greater than or equal to that of <span> <span>(Bbbk [overline{Q}])</span> </span>. Moreover, we also show counterexamples of this statement if we drop the assumption <span> <span>((S_2))</span> </span>.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140115449","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
Well-posedness of non-autonomous transport equation on metric graphs 度量图上非自治输运方程的好求性
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-03-06 DOI: 10.1007/s00233-024-10417-x
Christian Budde, Marjeta Kramar Fijavž
{"title":"Well-posedness of non-autonomous transport equation on metric graphs","authors":"Christian Budde, Marjeta Kramar Fijavž","doi":"10.1007/s00233-024-10417-x","DOIUrl":"https://doi.org/10.1007/s00233-024-10417-x","url":null,"abstract":"<p>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.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045409","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
Author Correction: Joint continuity in semitopological monoids and semilattices 作者更正：半拓扑单体和半网格中的联合连续性
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-02-26 DOI: 10.1007/s00233-024-10418-w
Alexander V. Osipov, Konstantin Kazachenko
{"title":"Author Correction: Joint continuity in semitopological monoids and semilattices","authors":"Alexander V. Osipov, Konstantin Kazachenko","doi":"10.1007/s00233-024-10418-w","DOIUrl":"https://doi.org/10.1007/s00233-024-10418-w","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140428412","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
Combinatorial results for semigroups of orientation-preserving and order-decreasing transformations 保向和阶减变换半群的组合结果
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-02-23 DOI: 10.1007/s00233-024-10413-1
{"title":"Combinatorial results for semigroups of orientation-preserving and order-decreasing transformations","authors":"","doi":"10.1007/s00233-024-10413-1","DOIUrl":"https://doi.org/10.1007/s00233-024-10413-1","url":null,"abstract":"<h3>Abstract</h3> <p>Let <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})</span> </span> be the semigroup consisting of all orientation-preserving and order-decreasing full transformations on the finite chain <span> <span>(X_{n}={1&lt;cdots &lt;n})</span> </span>, and let <span> <span>(N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}))</span> </span> be the subsemigroup consisting of all nilpotent elements of <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})</span> </span>. Moreover, for <span> <span>(1le rle n-1)</span> </span>, let <span> <span>$$begin{aligned} {{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r) ={alpha in {{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n},:, |textrm{im},(alpha )|le r}, end{aligned}$$</span> </span>and let <span> <span>(N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r)))</span> </span> be the subsemigroup consisting of all nilpotent elements of <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r))</span> </span>. In this paper, we compute the cardinalities of <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})</span> </span>, <span> <span>(N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}))</span> </span>, <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r))</span> </span> and <span> <span>(N({{mathscr {O}}{mathscr {P}}{mathscr {D}}}(n,r)))</span> </span>, and find their ranks. Moreover, for each idempotent <span> <span>(xi )</span> </span> in <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})</span> </span>, we show that <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n}(xi )={ alpha in {{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n} , alpha ^{m}=xi ,, text{ for } text{ some } ,, min {mathbb {N}} })</span> </span> is the maximal nilpotent subsemigroup of <span> <span>({{mathscr {O}}{mathscr {P}}{mathscr {D}}}_{n})</span> </span> with zero <span> <span>(xi )</span> </span>, and we find its cardinality and rank.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953366","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 nil-ai-semiring varieties 一些无爱音节变体
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-02-14 DOI: 10.1007/s00233-024-10411-3
{"title":"Some nil-ai-semiring varieties","authors":"","doi":"10.1007/s00233-024-10411-3","DOIUrl":"https://doi.org/10.1007/s00233-024-10411-3","url":null,"abstract":"<h3>Abstract</h3> <p>We study some nil-ai-semiring varieties. We establish a model for the free object in the variety <span> <span>(textbf{FC})</span> </span> 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 <span> <span>(P_{scriptstyle {dot{S}}_{c}(W)})</span> </span> of the finite nil-semigroup <span> <span>({dot{S}}_{c}(W))</span> </span> is nonfinitely based, where <em>W</em> is a finite set of words in the free commutative semigroup <span> <span>(X_{c}^{+})</span> </span> over an alphabet <em>X</em>, whenever the maximum of lengths of words in <em>W</em> is <span> <span>(kge 3)</span> </span> and <em>W</em> does not contain the <em>k</em>th power of a letter. This partially answers a problem raised by Jackson et al. (J Algebr 611: 211–245, 2022).</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752403","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 atoms of the set of generalized numerical semigroups with fixed corner element 论具有固定角元素的广义数值半群集合的原子
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-02-14 DOI: 10.1007/s00233-024-10412-2
Matheus Bernardini, Alonso S. Castellanos, Wanderson Tenório, Guilherme Tizziotti
{"title":"On atoms of the set of generalized numerical semigroups with fixed corner element","authors":"Matheus Bernardini, Alonso S. Castellanos, Wanderson Tenório, Guilherme Tizziotti","doi":"10.1007/s00233-024-10412-2","DOIUrl":"https://doi.org/10.1007/s00233-024-10412-2","url":null,"abstract":"<p>We study the atomic generalized numerical semigroups (GNSs), which naturally extend the concept of atomic numerical semigroups. We introduce the notion of corner special gap and we characterize the class of atomic GNS in terms of the cardinality of the set of corner special gaps and also in terms of a maximal property. Using this maximal property we present some properties concerning irreducibility of Frobenius GNSs. In particular, we provide sufficient conditions for certain Frobenius GNSs to be atom non-irreducible. Furthermore, we given necessary and sufficient conditions so that the maximal elements of a set of Frobenius GNSs with two fixed gaps to be all irreducible or not.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752378","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
Quantitative estimates for bounded holomorphic semigroups 有界全形半群的定量估计
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-02-12 DOI: 10.1007/s00233-024-10407-z
Tuomas Hytönen, Stefanos Lappas
{"title":"Quantitative estimates for bounded holomorphic semigroups","authors":"Tuomas Hytönen, Stefanos Lappas","doi":"10.1007/s00233-024-10407-z","DOIUrl":"https://doi.org/10.1007/s00233-024-10407-z","url":null,"abstract":"<p>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.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752525","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
Non-K3 Weierstrass numerical semigroups 非 K3 Weierstrass 数字半群
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2024-02-07 DOI: 10.1007/s00233-024-10406-0
Jiryo Komeda, Makiko Mase
{"title":"Non-K3 Weierstrass numerical semigroups","authors":"Jiryo Komeda, Makiko Mase","doi":"10.1007/s00233-024-10406-0","DOIUrl":"https://doi.org/10.1007/s00233-024-10406-0","url":null,"abstract":"<p>We generalize the result of Reid (J Lond Math Soc 13:454–458, 1976), namely, we prove that a curve of genus <span>(geqq g^2+4g+6)</span> having a double cover of a hyperelliptic curve of genus <span>(ggeqq 2)</span> 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 <i>H</i> is said to be <i>Weierstrass</i> if there exists a pointed non-singular curve (<i>C</i>, <i>P</i>) such that <i>H</i> consists of non-negative integers which are the pole orders at <i>P</i> of a rational function on <i>C</i> having a pole only at <i>P</i>. We call the numerical semigroup <i>K3</i> if we can take the curve <i>C</i> as a curve on some K3 surface. A <i>non-K3 numerical semigroup</i> means that it cannot be attained by a pointed non-singular curve on any K3 surface. We also give infinite sequences of non-K3 Weierstrass numerical semigroups.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752533","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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