Axioms for unary semigroups via division operations
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
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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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 |
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instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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