Pub Date : 2023-10-02DOI: 10.1007/s00233-023-10387-6
Fabián Arias, Jerson Borja, Calixto Rhenals
{"title":"The Frobenius problem for numerical semigroups generated by sequences of the form $$ca^n-d$$","authors":"Fabián Arias, Jerson Borja, Calixto Rhenals","doi":"10.1007/s00233-023-10387-6","DOIUrl":"https://doi.org/10.1007/s00233-023-10387-6","url":null,"abstract":"","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135829067","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}
Pub Date : 2023-10-01DOI: 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}
Pub Date : 2023-10-01DOI: 10.1007/s00233-023-10385-8
Felix Gotti, Joseph Vulakh
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.
{"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}
Pub Date : 2023-10-01DOI: 10.1007/s00233-023-10389-4
Luís Oliveira
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 $$F_{1}$$ F1 weakly generated by x such that all other regular semigroups weakly generated by x are homomorphic images of $$F_{1}$$ F1 . We define $$F_{1}$$ F1 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 $$F_{1}$$ F1 . In particular, we show that the ‘free regular semigroup $${textrm{FI}}_2$$ FI2 weakly generated by two idempotents’ is isomorphic to a regular subsemigroup of $$F_{1}$$ F1 weakly generated by $${xx',x'x}$$ {xx′,x′x} .
摘要研究了由单元素x弱生成的正则半群，即不含x的正则子半群。我们证明了存在一个由x弱生成的正则半群$$F_{1}$$ f1，使得其他所有由x弱生成的正则半群都是$$F_{1}$$ f1的同态象。我们使用一种表示来定义$$F_{1}$$ f1，其中生成器集和关系集都是无限的。然而，这个演讲的问题是可以确定的。本文给出了同余类的一个标准形式，并说明了如何得到它。本文最后对$$F_{1}$$ f1的结构进行了研究。特别地，我们证明了由两个幂等元弱生成的自由正则半群$${textrm{FI}}_2$$ FI 2与由$${xx',x'x}$$ x x '， x 弱生成的$$F_{1}$$ f1的正则子半群是同构的。{}
{"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}
Pub Date : 2023-10-01DOI: 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}
Pub Date : 2023-09-25DOI: 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}
Pub Date : 2023-09-20DOI: 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}
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