Conjugation in semigroups

Detalhes bibliográficos
Autor(a) principal: Araújo, João
Data de Publicação: 2014
Outros Autores: Konieczny, Janusz, Malheiro, António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/3798
Resumo: The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.
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spelling Conjugation in semigroupsSemigroupsConjugacyTransformationsDirected graphsWell-founded relationsThe action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.Repositório AbertoAraújo, JoãoKonieczny, JanuszMalheiro, António2015-03-23T15:23:41Z20142014-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3798engAraújo, João; Konieczny, Janusz; Malheiro, António - Conjugation in semigroups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 403 (2014), p. 1-340021-869310.1016/j.jalgebra.2013.12.025info: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:RCAAP2023-11-16T15:19:10Zoai:repositorioaberto.uab.pt:10400.2/3798Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:44:59.657487Repositório 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 Conjugation in semigroups
title Conjugation in semigroups
spellingShingle Conjugation in semigroups
Araújo, João
Semigroups
Conjugacy
Transformations
Directed graphs
Well-founded relations
title_short Conjugation in semigroups
title_full Conjugation in semigroups
title_fullStr Conjugation in semigroups
title_full_unstemmed Conjugation in semigroups
title_sort Conjugation in semigroups
author Araújo, João
author_facet Araújo, João
Konieczny, Janusz
Malheiro, António
author_role author
author2 Konieczny, Janusz
Malheiro, António
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Araújo, João
Konieczny, Janusz
Malheiro, António
dc.subject.por.fl_str_mv Semigroups
Conjugacy
Transformations
Directed graphs
Well-founded relations
topic Semigroups
Conjugacy
Transformations
Directed graphs
Well-founded relations
description The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-01-01T00:00:00Z
2015-03-23T15:23:41Z
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/10400.2/3798
url http://hdl.handle.net/10400.2/3798
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Araújo, João; Konieczny, Janusz; Malheiro, António - Conjugation in semigroups. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 403 (2014), p. 1-34
0021-8693
10.1016/j.jalgebra.2013.12.025
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_str RCAAP
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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