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The Frobenius problem for numerical semigroups generated by sequences of the form $$ca^n-d$$ 一类数列生成的数值半群的Frobenius问题 $$ca^n-d$$
3区 数学
Semigroup Forum Pub Date : 2023-10-02 DOI: 10.1007/s00233-023-10387-6
Fabián Arias, Jerson Borja, Calixto Rhenals
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引用次数: 0
Editorial note 编辑说明
IF 0.7 3区 数学
Semigroup Forum Pub Date : 2023-10-01 DOI: 10.1007/s00233-023-10398-3
Mikhail Volkov
{"title":"Editorial note","authors":"Mikhail Volkov","doi":"10.1007/s00233-023-10398-3","DOIUrl":"https://doi.org/10.1007/s00233-023-10398-3","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"19 1","pages":"579 - 579"},"PeriodicalIF":0.7,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330028","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
Representations and identities of Baxter monoids with involution 具有对合的Baxter一元群的表示和恒等式
3区 数学
Semigroup Forum Pub Date : 2023-10-01 DOI: 10.1007/s00233-023-10388-5
Bin Bin Han, Wen Ting Zhang, Yan Feng Luo, Jin Xing Zhao
{"title":"Representations and identities of Baxter monoids with involution","authors":"Bin Bin Han, Wen Ting Zhang, Yan Feng Luo, Jin Xing Zhao","doi":"10.1007/s00233-023-10388-5","DOIUrl":"https://doi.org/10.1007/s00233-023-10388-5","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135708105","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 atomic structure of torsion-free monoids 关于无扭转模群的原子结构
3区 数学
Semigroup Forum Pub Date : 2023-10-01 DOI: 10.1007/s00233-023-10385-8
Felix Gotti, Joseph Vulakh
{"title":"On the atomic structure of torsion-free monoids","authors":"Felix Gotti, Joseph Vulakh","doi":"10.1007/s00233-023-10385-8","DOIUrl":"https://doi.org/10.1007/s00233-023-10385-8","url":null,"abstract":"Abstract Let M be a cancellative and commutative (additive) monoid. The monoid M is atomic if every non-invertible element can be written as a sum of irreducible elements, which are also called atoms. Also, M satisfies the ascending chain condition on principal ideals (ACCP) if every increasing sequence of principal ideals (under inclusion) becomes constant from one point on. In the first part of this paper, we characterize torsion-free monoids that satisfy the ACCP as those torsion-free monoids whose submonoids are all atomic. A submonoid of the nonnegative cone of a totally ordered abelian group is often called a positive monoid. Every positive monoid is clearly torsion-free. In the second part of this paper, we study the atomic structure of certain classes of positive monoids.","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134934169","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: 7
Regular semigroups weakly generated by one element 由一个元素弱生成的正则半群
3区 数学
Semigroup Forum Pub Date : 2023-10-01 DOI: 10.1007/s00233-023-10389-4
Luís Oliveira
{"title":"Regular semigroups weakly generated by one element","authors":"Luís Oliveira","doi":"10.1007/s00233-023-10389-4","DOIUrl":"https://doi.org/10.1007/s00233-023-10389-4","url":null,"abstract":"Abstract In this paper we study the regular semigroups weakly generated by a single element x , that is, with no proper regular subsemigroup containing x . We show there exists a regular semigroup $$F_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> weakly generated by x such that all other regular semigroups weakly generated by x are homomorphic images of $$F_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> . We define $$F_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> using a presentation where both sets of generators and relations are infinite. Nevertheless, the word problem for this presentation is decidable. We describe a canonical form for the congruence classes given by this presentation, and explain how to obtain it. We end the paper studying the structure of $$F_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> . In particular, we show that the ‘free regular semigroup $${textrm{FI}}_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mtext>FI</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> weakly generated by two idempotents’ is isomorphic to a regular subsemigroup of $$F_{1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> weakly generated by $${xx',x'x}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>x</mml:mi> <mml:msup> <mml:mi>x</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>x</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>x</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> .","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135705763","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: 1
A new generation criterion theorem for $$C_0$$-semigroups implying a generalization of Kaiser–Weis–Batty’s perturbation theorem 推广Kaiser-Weis-Batty摄动定理的$$C_0$$ -半群新一代判据定理
3区 数学
Semigroup Forum Pub Date : 2023-10-01 DOI: 10.1007/s00233-023-10391-w
Hatem Megdiche
{"title":"A new generation criterion theorem for $$C_0$$-semigroups implying a generalization of Kaiser–Weis–Batty’s perturbation theorem","authors":"Hatem Megdiche","doi":"10.1007/s00233-023-10391-w","DOIUrl":"https://doi.org/10.1007/s00233-023-10391-w","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135655565","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
Publisher Correction to: Variational principle for BS-dimension of subsets of finitely generated free semigroup actions 有限生成的自由半群动作子集的bs维的变分原理
3区 数学
Semigroup Forum Pub Date : 2023-09-26 DOI: 10.1007/s00233-023-10386-7
Zhumin Ding, Xin Liu
{"title":"Publisher Correction to: Variational principle for BS-dimension of subsets of finitely generated free semigroup actions","authors":"Zhumin Ding, Xin Liu","doi":"10.1007/s00233-023-10386-7","DOIUrl":"https://doi.org/10.1007/s00233-023-10386-7","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134886646","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
Normal subsemigroups of finite transformation semigroups 有限变换半群的正规子半群
3区 数学
Semigroup Forum Pub Date : 2023-09-25 DOI: 10.1007/s00233-023-10383-w
Janusz Konieczny
{"title":"Normal subsemigroups of finite transformation semigroups","authors":"Janusz Konieczny","doi":"10.1007/s00233-023-10383-w","DOIUrl":"https://doi.org/10.1007/s00233-023-10383-w","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135771011","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
The quantale of order-preserving maps of a completely distributive lattice 完全分布格的保序映射的量子化
3区 数学
Semigroup Forum Pub Date : 2023-09-25 DOI: 10.1007/s00233-023-10384-9
Hongwei Wu
{"title":"The quantale of order-preserving maps of a completely distributive lattice","authors":"Hongwei Wu","doi":"10.1007/s00233-023-10384-9","DOIUrl":"https://doi.org/10.1007/s00233-023-10384-9","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135771198","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
Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes 属于规定格林等价类的半群中的外逆
3区 数学
Semigroup Forum Pub Date : 2023-09-20 DOI: 10.1007/s00233-023-10382-x
Miroslav Ćirić, Jelena Ignjatović, Predrag Stanimirović
{"title":"Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes","authors":"Miroslav Ćirić, Jelena Ignjatović, Predrag Stanimirović","doi":"10.1007/s00233-023-10382-x","DOIUrl":"https://doi.org/10.1007/s00233-023-10382-x","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306651","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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