Semigroup ForumPub 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}
Semigroup ForumPub 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}
Semigroup ForumPub Date : 2023-10-01DOI: 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}
Semigroup ForumPub Date : 2023-10-01DOI: 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}
Semigroup ForumPub 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}
Semigroup ForumPub 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}
Semigroup ForumPub 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}