Centralizers in the full transformation semigroup

Detalhes bibliográficos
Autor(a) principal: Araújo, João
Data de Publicação: 2013
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/10400.2/3795
Resumo: For an arbitrary set X (finite or infinite), denote by T (X) the semigroup of full transformations on X. For α ∈ T (X), let C(α) = {β ∈ T (X) : αβ = βα} be the centralizer of α in T (X). The aim of this paper is to characterize the elements of C(α). The characterization is obtained by decomposing α as a join of connected partial transformations on X and analyzing the homomorphisms of the directed graphs representing the connected transformations. The paper closes with a number of open problems and suggestions of future investigations.
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spelling Centralizers in the full transformation semigroupFull transformationsCentralizersDigraph homomorphismsFor an arbitrary set X (finite or infinite), denote by T (X) the semigroup of full transformations on X. For α ∈ T (X), let C(α) = {β ∈ T (X) : αβ = βα} be the centralizer of α in T (X). The aim of this paper is to characterize the elements of C(α). The characterization is obtained by decomposing α as a join of connected partial transformations on X and analyzing the homomorphisms of the directed graphs representing the connected transformations. The paper closes with a number of open problems and suggestions of future investigations.Repositório AbertoAraújo, JoãoKonieczny, Janusz2015-03-23T14:28:35Z20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3795engAraújo, João; Konieczny, Janusz - Centralizers in the full transformation semigroup. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 86, nº 1 (2013), p. 1-320037-191210.1007/s00233-012-9424-0info: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:10400.2/3795Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:44:59.881744Repositório 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 Centralizers in the full transformation semigroup
title Centralizers in the full transformation semigroup
spellingShingle Centralizers in the full transformation semigroup
Araújo, João
Full transformations
Centralizers
Digraph homomorphisms
title_short Centralizers in the full transformation semigroup
title_full Centralizers in the full transformation semigroup
title_fullStr Centralizers in the full transformation semigroup
title_full_unstemmed Centralizers in the full transformation semigroup
title_sort Centralizers in the full transformation semigroup
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 Full transformations
Centralizers
Digraph homomorphisms
topic Full transformations
Centralizers
Digraph homomorphisms
description For an arbitrary set X (finite or infinite), denote by T (X) the semigroup of full transformations on X. For α ∈ T (X), let C(α) = {β ∈ T (X) : αβ = βα} be the centralizer of α in T (X). The aim of this paper is to characterize the elements of C(α). The characterization is obtained by decomposing α as a join of connected partial transformations on X and analyzing the homomorphisms of the directed graphs representing the connected transformations. The paper closes with a number of open problems and suggestions of future investigations.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01T00:00:00Z
2015-03-23T14:28:35Z
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/10400.2/3795
url http://hdl.handle.net/10400.2/3795
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Araújo, João; Konieczny, Janusz - Centralizers in the full transformation semigroup. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 86, nº 1 (2013), p. 1-32
0037-1912
10.1007/s00233-012-9424-0
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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