Automorphism groups of centralizers of idempotents

Detalhes bibliográficos
Autor(a) principal: Araújo, João
Data de Publicação: 2003
Outros Autores: Konieczny, Janusz
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/3809
Resumo: For a set X, an equivalence relation Ω on X, and a cross-section R of the partition X/Ω, consider the following subsemigroup of the semigroup T(X) of full transformations on X:T(X, Ω,R) = {a 2 T(X) : Ra μ R and (x, y) 2 Ω ) (xa, ya) 2 Ω}. The semigroup T(X, Ω,R) is the centralizer of the idempotent transformation with kernel Ω and image R. We prove that the automorphisms of T(X, Ω,R) are the inner automorphisms induced by the units of T(X, Ω,R) and that the automorphism group of T(X, Ω,R) is isomorphic to the group of units of T(X, Ω,R).
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spelling Automorphism groups of centralizers of idempotentsAutomorphism groupTransformation semigroupInner automorphismCentralizerDempotentFor a set X, an equivalence relation Ω on X, and a cross-section R of the partition X/Ω, consider the following subsemigroup of the semigroup T(X) of full transformations on X:T(X, Ω,R) = {a 2 T(X) : Ra μ R and (x, y) 2 Ω ) (xa, ya) 2 Ω}. The semigroup T(X, Ω,R) is the centralizer of the idempotent transformation with kernel Ω and image R. We prove that the automorphisms of T(X, Ω,R) are the inner automorphisms induced by the units of T(X, Ω,R) and that the automorphism group of T(X, Ω,R) is isomorphic to the group of units of T(X, Ω,R).Repositório AbertoAraújo, JoãoKonieczny, Janusz2015-03-24T11:55:11Z20032003-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3809engAraújo, João; Konieczny, Janusz - Automorphism groups of centralizers of idempotents. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 269, nº 1 (2003), p. 1-120021-869310.1016/S0021-8693(03)00499-Xinfo: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:RCAAP2023-11-16T15:19:12Zoai:repositorioaberto.uab.pt:10400.2/3809Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:45:00.577164Repositório 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 Automorphism groups of centralizers of idempotents
title Automorphism groups of centralizers of idempotents
spellingShingle Automorphism groups of centralizers of idempotents
Araújo, João
Automorphism group
Transformation semigroup
Inner automorphism
Centralizer
Dempotent
title_short Automorphism groups of centralizers of idempotents
title_full Automorphism groups of centralizers of idempotents
title_fullStr Automorphism groups of centralizers of idempotents
title_full_unstemmed Automorphism groups of centralizers of idempotents
title_sort Automorphism groups of centralizers of idempotents
author Araújo, João
author_facet Araújo, João
Konieczny, Janusz
author_role author
author2 Konieczny, Janusz
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Araújo, João
Konieczny, Janusz
dc.subject.por.fl_str_mv Automorphism group
Transformation semigroup
Inner automorphism
Centralizer
Dempotent
topic Automorphism group
Transformation semigroup
Inner automorphism
Centralizer
Dempotent
description For a set X, an equivalence relation Ω on X, and a cross-section R of the partition X/Ω, consider the following subsemigroup of the semigroup T(X) of full transformations on X:T(X, Ω,R) = {a 2 T(X) : Ra μ R and (x, y) 2 Ω ) (xa, ya) 2 Ω}. The semigroup T(X, Ω,R) is the centralizer of the idempotent transformation with kernel Ω and image R. We prove that the automorphisms of T(X, Ω,R) are the inner automorphisms induced by the units of T(X, Ω,R) and that the automorphism group of T(X, Ω,R) is isomorphic to the group of units of T(X, Ω,R).
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-01-01T00:00:00Z
2015-03-24T11:55:11Z
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/10400.2/3809
url http://hdl.handle.net/10400.2/3809
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Araújo, João; Konieczny, Janusz - Automorphism groups of centralizers of idempotents. "Journal of Algebra" [Em linha]. ISSN 0021-8693. Vol. 269, nº 1 (2003), p. 1-12
0021-8693
10.1016/S0021-8693(03)00499-X
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)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
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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