Some orthodox monoids with associate inverse subsemigroups

Detalhes bibliográficos
Autor(a) principal: Billhardt, Bernd
Data de Publicação: 2011
Outros Autores: Giraldes, Emília, Smith, M. Paula Marques, Martins, Paula Mendes
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/11632
Resumo: By an associate inverse subsemigroup of a regular semigroup $S$ we mean a subsemigroup $T$ of $S$ containing a least associate of each $x \in S$, in relation to the natural partial order $\leq_S$ in $S$. In this paper we investigate a class of orthodox monoids with an associate inverse subsemigroup and obtain a known description of uniquely unit regular orthodox semigroups as a corollary. Also, by considering a more general situation, we identify the homomorphic image of a kind of semidirect product of a band with identity by an inverse monoid, thus extending a known result for unit regular orthodox semigroups.
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spelling Some orthodox monoids with associate inverse subsemigroupsAssociate inverse subsemigroupOrthodox semigroupF-semigroupsScience & TechnologyBy an associate inverse subsemigroup of a regular semigroup $S$ we mean a subsemigroup $T$ of $S$ containing a least associate of each $x \in S$, in relation to the natural partial order $\leq_S$ in $S$. In this paper we investigate a class of orthodox monoids with an associate inverse subsemigroup and obtain a known description of uniquely unit regular orthodox semigroups as a corollary. Also, by considering a more general situation, we identify the homomorphic image of a kind of semidirect product of a band with identity by an inverse monoid, thus extending a known result for unit regular orthodox semigroups.Portuguese Foundation for Science and Technology (FCT) through the Research Centre CMATTaylor and FrancisUniversidade do MinhoBillhardt, BerndGiraldes, EmíliaSmith, M. Paula MarquesMartins, Paula Mendes2011-012011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/11632eng"Communications in Algebra". ISSN 0092-7872. 39:1 (2011) 32-49.0092-787210.1080/00927870903428254http://dx.doi.org/10.1080/00927870903428254info: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:RCAAP2023-07-21T12:10:58Zoai:repositorium.sdum.uminho.pt:1822/11632Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:02:40.744745Repositório 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 Some orthodox monoids with associate inverse subsemigroups
title Some orthodox monoids with associate inverse subsemigroups
spellingShingle Some orthodox monoids with associate inverse subsemigroups
Billhardt, Bernd
Associate inverse subsemigroup
Orthodox semigroup
F-semigroups
Science & Technology
title_short Some orthodox monoids with associate inverse subsemigroups
title_full Some orthodox monoids with associate inverse subsemigroups
title_fullStr Some orthodox monoids with associate inverse subsemigroups
title_full_unstemmed Some orthodox monoids with associate inverse subsemigroups
title_sort Some orthodox monoids with associate inverse subsemigroups
author Billhardt, Bernd
author_facet Billhardt, Bernd
Giraldes, Emília
Smith, M. Paula Marques
Martins, Paula Mendes
author_role author
author2 Giraldes, Emília
Smith, M. Paula Marques
Martins, Paula Mendes
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Billhardt, Bernd
Giraldes, Emília
Smith, M. Paula Marques
Martins, Paula Mendes
dc.subject.por.fl_str_mv Associate inverse subsemigroup
Orthodox semigroup
F-semigroups
Science & Technology
topic Associate inverse subsemigroup
Orthodox semigroup
F-semigroups
Science & Technology
description By an associate inverse subsemigroup of a regular semigroup $S$ we mean a subsemigroup $T$ of $S$ containing a least associate of each $x \in S$, in relation to the natural partial order $\leq_S$ in $S$. In this paper we investigate a class of orthodox monoids with an associate inverse subsemigroup and obtain a known description of uniquely unit regular orthodox semigroups as a corollary. Also, by considering a more general situation, we identify the homomorphic image of a kind of semidirect product of a band with identity by an inverse monoid, thus extending a known result for unit regular orthodox semigroups.
publishDate 2011
dc.date.none.fl_str_mv 2011-01
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/1822/11632
url http://hdl.handle.net/1822/11632
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Communications in Algebra". ISSN 0092-7872. 39:1 (2011) 32-49.
0092-7872
10.1080/00927870903428254
http://dx.doi.org/10.1080/00927870903428254
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 Taylor and Francis
publisher.none.fl_str_mv Taylor and Francis
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
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