Axioms for unary semigroups via division operations

Detalhes bibliográficos
Autor(a) principal: Araújo, João
Data de Publicação: 2012
Outros Autores: Kinyon, Michael
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/3796
Resumo: When a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.
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spelling Axioms for unary semigroups via division operationsBigroupoidClifford semigroupsCompletely regularE-inversive semigroupsInverse semigroupsWhen a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.Repositório AbertoAraújo, JoãoKinyon, Michael2015-03-23T14:31:59Z20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3796engAraújo, João; Kinyon, Michael - Axioms for unary semigroups via division operations. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 40, nº 2 (2012), p. 1-170092-787210.1080/00927872.2010.536604info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:19:11Zoai:repositorioaberto.uab.pt:10400.2/3796Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:45:00.015661Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Axioms for unary semigroups via division operations
title Axioms for unary semigroups via division operations
spellingShingle Axioms for unary semigroups via division operations
Araújo, João
Bigroupoid
Clifford semigroups
Completely regular
E-inversive semigroups
Inverse semigroups
title_short Axioms for unary semigroups via division operations
title_full Axioms for unary semigroups via division operations
title_fullStr Axioms for unary semigroups via division operations
title_full_unstemmed Axioms for unary semigroups via division operations
title_sort Axioms for unary semigroups via division operations
author Araújo, João
author_facet Araújo, João
Kinyon, Michael
author_role author
author2 Kinyon, Michael
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Araújo, João
Kinyon, Michael
dc.subject.por.fl_str_mv Bigroupoid
Clifford semigroups
Completely regular
E-inversive semigroups
Inverse semigroups
topic Bigroupoid
Clifford semigroups
Completely regular
E-inversive semigroups
Inverse semigroups
description When a semigroup has a unary operation, it is possible to define two bin ary operations, namely, left and right division. In addition it is well known that groups can be defined in terms of those two divisions. The aim of this paper is to extend those results to other classes of unary semigroups. In the first part of the paper we provide characterizations for several classes of unary semigroups, including (a special class of) E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division. In the second part we solve a problem that was posed elsewhere. The paper closes with a list of open problems.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-01-01T00:00:00Z
2015-03-23T14:31:59Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/3796
url http://hdl.handle.net/10400.2/3796
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Araújo, João; Kinyon, Michael - Axioms for unary semigroups via division operations. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 40, nº 2 (2012), p. 1-17
0092-7872
10.1080/00927872.2010.536604
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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