Semigroups of transformations preserving an equivalence relation and a cross-section
Autor(a) principal: | |
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Data de Publicação: | 2004 |
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/10400.2/3806 |
Resumo: | For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T (X, ρ,R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y) ∈ ρ then (xa, ya) ∈ ρ) and R (if r ∈ R then ra ∈ R). The semigroup T (X, ρ,R) is the centralizer of the idempotent transformation with kernel ρ and image R. We determine the structure of T (X, ρ,R) in terms of Green’s relations, describe the regular elements of T (X, ρ,R), and determine the following classes of the semigroups T (X, ρ,R): regular, abundant, inverse, and completely regular. |
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Semigroups of transformations preserving an equivalence relation and a cross-sectionTransformationEquivalence relationIdempotentCentralizer20M20For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T (X, ρ,R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y) ∈ ρ then (xa, ya) ∈ ρ) and R (if r ∈ R then ra ∈ R). The semigroup T (X, ρ,R) is the centralizer of the idempotent transformation with kernel ρ and image R. We determine the structure of T (X, ρ,R) in terms of Green’s relations, describe the regular elements of T (X, ρ,R), and determine the following classes of the semigroups T (X, ρ,R): regular, abundant, inverse, and completely regular.Repositório AbertoAraújo, JoãoKonieczny, Janusz2015-03-24T10:16:57Z20042004-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/3806engAraújo, João; Konieczny, Janusz - Semigroups of transformations preserving an equivalence relation and a cross-section. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 32 (2004), p. 1-170092-787210.1081/AGB-120029913info: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:10400.2/3806Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:45:00.323566Repositório 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 |
Semigroups of transformations preserving an equivalence relation and a cross-section |
title |
Semigroups of transformations preserving an equivalence relation and a cross-section |
spellingShingle |
Semigroups of transformations preserving an equivalence relation and a cross-section Araújo, João Transformation Equivalence relation Idempotent Centralizer 20M20 |
title_short |
Semigroups of transformations preserving an equivalence relation and a cross-section |
title_full |
Semigroups of transformations preserving an equivalence relation and a cross-section |
title_fullStr |
Semigroups of transformations preserving an equivalence relation and a cross-section |
title_full_unstemmed |
Semigroups of transformations preserving an equivalence relation and a cross-section |
title_sort |
Semigroups of transformations preserving an equivalence relation and a cross-section |
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 |
Transformation Equivalence relation Idempotent Centralizer 20M20 |
topic |
Transformation Equivalence relation Idempotent Centralizer 20M20 |
description |
For a set X, an equivalence relation ρ on X, and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T (X, ρ,R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y) ∈ ρ then (xa, ya) ∈ ρ) and R (if r ∈ R then ra ∈ R). The semigroup T (X, ρ,R) is the centralizer of the idempotent transformation with kernel ρ and image R. We determine the structure of T (X, ρ,R) in terms of Green’s relations, describe the regular elements of T (X, ρ,R), and determine the following classes of the semigroups T (X, ρ,R): regular, abundant, inverse, and completely regular. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004 2004-01-01T00:00:00Z 2015-03-24T10:16:57Z |
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/10400.2/3806 |
url |
http://hdl.handle.net/10400.2/3806 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Araújo, João; Konieczny, Janusz - Semigroups of transformations preserving an equivalence relation and a cross-section. "Communications in Algebra" [Em linha]. ISSN 0092-7872 (Print) 1532-4125 (Online). Vol. 32 (2004), p. 1-17 0092-7872 10.1081/AGB-120029913 |
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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1799135021446987776 |