Regular centralizers of idempotent transformations
Autor(a) principal: | |
---|---|
Data de Publicação: | 2011 |
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/10400.2/2001 |
Resumo: | Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id X )=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id X ) contains all non-invertible transformations in C(id X ). This paper generalizes this result to C(ε), an arbitrary regular centralizer of an idempotent transformation ε∈T(X), by describing the subsemigroup generated by the idempotents of C(ε). As a corollary we obtain that the subsemigroup generated by the idempotents of a regular C(ε) contains all non-invertible transformations in C(ε) if and only if ε is the identity or a constant transformation. |
id |
RCAP_9e6daf4372d87cd5c220d2d477e234a6 |
---|---|
oai_identifier_str |
oai:repositorioaberto.uab.pt:10400.2/2001 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Regular centralizers of idempotent transformationsIdempotent transformationsRegular centralizersGeneratorsDenote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id X )=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id X ) contains all non-invertible transformations in C(id X ). This paper generalizes this result to C(ε), an arbitrary regular centralizer of an idempotent transformation ε∈T(X), by describing the subsemigroup generated by the idempotents of C(ε). As a corollary we obtain that the subsemigroup generated by the idempotents of a regular C(ε) contains all non-invertible transformations in C(ε) if and only if ε is the identity or a constant transformation.Springer VerlagRepositório AbertoAndré, JorgeAraújo, JoãoKonieczny, Janusz2011-12-19T11:57:22Z20112011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/2001engAndré, Jorge; Araújo, João; Konieczny, Janusz - Regular centralizers of idempotent transformations. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 82, nº 2 (Apr. 2011), p. 307-318DOI 10.1007/s00233-010-9274-6info: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:RCAAP2023-11-16T15:15:13Zoai:repositorioaberto.uab.pt:10400.2/2001Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:43:36.638334Repositório 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 |
Regular centralizers of idempotent transformations |
title |
Regular centralizers of idempotent transformations |
spellingShingle |
Regular centralizers of idempotent transformations André, Jorge Idempotent transformations Regular centralizers Generators |
title_short |
Regular centralizers of idempotent transformations |
title_full |
Regular centralizers of idempotent transformations |
title_fullStr |
Regular centralizers of idempotent transformations |
title_full_unstemmed |
Regular centralizers of idempotent transformations |
title_sort |
Regular centralizers of idempotent transformations |
author |
André, Jorge |
author_facet |
André, Jorge Araújo, João Konieczny, Janusz |
author_role |
author |
author2 |
Araújo, João Konieczny, Janusz |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
André, Jorge Araújo, João Konieczny, Janusz |
dc.subject.por.fl_str_mv |
Idempotent transformations Regular centralizers Generators |
topic |
Idempotent transformations Regular centralizers Generators |
description |
Denote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id X )=T(X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(id X ) contains all non-invertible transformations in C(id X ). This paper generalizes this result to C(ε), an arbitrary regular centralizer of an idempotent transformation ε∈T(X), by describing the subsemigroup generated by the idempotents of C(ε). As a corollary we obtain that the subsemigroup generated by the idempotents of a regular C(ε) contains all non-invertible transformations in C(ε) if and only if ε is the identity or a constant transformation. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011-12-19T11:57:22Z 2011 2011-01-01T00:00:00Z |
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/10400.2/2001 |
url |
http://hdl.handle.net/10400.2/2001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
André, Jorge; Araújo, João; Konieczny, Janusz - Regular centralizers of idempotent transformations. "Semigroup Forum" [Em linha]. ISSN 0037-1912 (Print) 1432-2137 (Online). Vol. 82, nº 2 (Apr. 2011), p. 307-318 DOI 10.1007/s00233-010-9274-6 |
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.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
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 |
repository.mail.fl_str_mv |
|
_version_ |
1799135003594981376 |