F-regular semigroups
Autor(a) principal: | |
---|---|
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/1822/7449 |
Resumo: | A semigroup S is called F-regular if S is regular and if there exists a group congruence rho on S such that every rho-class contains a greatest element with respect to the natural partial order of S (see [K.S. Nambooripad, Proc. Edinburgh Math. Soc. 23 (1980) 249-260]). These semigroups were investigated in [C.C. Edwards, Semigroup Forum 19 (1980) 331-345] where a description similar to the F-inverse case (see [R. McFadden, L. O'Carroll, Proc. London Math. Soc. 22 (1971) 652-666]) is given. Further characterizations of F-regular semigroups, including an axiomatic one, are provided. The main objective is to give a new representation of such semigroups by means of Szendrei triples (see [M. Szendrei, Acta Sci. Math. 51 (1987) 229-249]). The particular case of F-regular semigroups S satisfying the identity (xy)* = y*x*, where x* epsilon S denotes the greatest element of the rho-class containing x epsilon S, is considered. Also the F-inversive semigroups, for which this identity holds, are characterized. (C) 2004 Elsevier Inc. All rights reserved. |
id |
RCAP_4b64420cbd7452c00135fa1565a2ba07 |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/7449 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
F-regular semigroupsGroup-congruenceCongruence-classRegular semigroupNatural partial orderScience & TechnologyA semigroup S is called F-regular if S is regular and if there exists a group congruence rho on S such that every rho-class contains a greatest element with respect to the natural partial order of S (see [K.S. Nambooripad, Proc. Edinburgh Math. Soc. 23 (1980) 249-260]). These semigroups were investigated in [C.C. Edwards, Semigroup Forum 19 (1980) 331-345] where a description similar to the F-inverse case (see [R. McFadden, L. O'Carroll, Proc. London Math. Soc. 22 (1971) 652-666]) is given. Further characterizations of F-regular semigroups, including an axiomatic one, are provided. The main objective is to give a new representation of such semigroups by means of Szendrei triples (see [M. Szendrei, Acta Sci. Math. 51 (1987) 229-249]). The particular case of F-regular semigroups S satisfying the identity (xy)* = y*x*, where x* epsilon S denotes the greatest element of the rho-class containing x epsilon S, is considered. Also the F-inversive semigroups, for which this identity holds, are characterized. (C) 2004 Elsevier Inc. All rights reserved.Fundação para a Ciência e a Tecnologia (FCT) - POCTI.ElsevierUniversidade do MinhoSmith, M. Paula MarquesGiraldes, E.Mitsch, H.20042004-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/7449eng"Journal of Algebra". ISSN 0021- 8693. 247:2 (2004) 491-510.0021- 869310.1016/j.jalgebra.2003.09.050http://www.sciencedirect.com/science?_ob= ArticleURL&_udi=B6WH2-4BP3JHP-1&_user= 10&_coverDate=04%2F15%2F2004&_alid= 664478190&_rdoc=1&_fmt=summary&_orig= search&_cdi=6838&_sort=d&_docanchor= &view=c&_ct=1&_acct=C000050221&_version= 1&_urlVersion=0&_userid=10&md5= b96ebda0467adad139ba92827e53789ainfo: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:RCAAP2023-07-21T12:13:15Zoai:repositorium.sdum.uminho.pt:1822/7449Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:05:18.595969Repositório 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 |
F-regular semigroups |
title |
F-regular semigroups |
spellingShingle |
F-regular semigroups Smith, M. Paula Marques Group-congruence Congruence-class Regular semigroup Natural partial order Science & Technology |
title_short |
F-regular semigroups |
title_full |
F-regular semigroups |
title_fullStr |
F-regular semigroups |
title_full_unstemmed |
F-regular semigroups |
title_sort |
F-regular semigroups |
author |
Smith, M. Paula Marques |
author_facet |
Smith, M. Paula Marques Giraldes, E. Mitsch, H. |
author_role |
author |
author2 |
Giraldes, E. Mitsch, H. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Smith, M. Paula Marques Giraldes, E. Mitsch, H. |
dc.subject.por.fl_str_mv |
Group-congruence Congruence-class Regular semigroup Natural partial order Science & Technology |
topic |
Group-congruence Congruence-class Regular semigroup Natural partial order Science & Technology |
description |
A semigroup S is called F-regular if S is regular and if there exists a group congruence rho on S such that every rho-class contains a greatest element with respect to the natural partial order of S (see [K.S. Nambooripad, Proc. Edinburgh Math. Soc. 23 (1980) 249-260]). These semigroups were investigated in [C.C. Edwards, Semigroup Forum 19 (1980) 331-345] where a description similar to the F-inverse case (see [R. McFadden, L. O'Carroll, Proc. London Math. Soc. 22 (1971) 652-666]) is given. Further characterizations of F-regular semigroups, including an axiomatic one, are provided. The main objective is to give a new representation of such semigroups by means of Szendrei triples (see [M. Szendrei, Acta Sci. Math. 51 (1987) 229-249]). The particular case of F-regular semigroups S satisfying the identity (xy)* = y*x*, where x* epsilon S denotes the greatest element of the rho-class containing x epsilon S, is considered. Also the F-inversive semigroups, for which this identity holds, are characterized. (C) 2004 Elsevier Inc. All rights reserved. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004 2004-01-01T00:00:00Z |
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/1822/7449 |
url |
http://hdl.handle.net/1822/7449 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"Journal of Algebra". ISSN 0021- 8693. 247:2 (2004) 491-510. 0021- 8693 10.1016/j.jalgebra.2003.09.050 http://www.sciencedirect.com/science?_ob= ArticleURL&_udi=B6WH2-4BP3JHP-1&_user= 10&_coverDate=04%2F15%2F2004&_alid= 664478190&_rdoc=1&_fmt=summary&_orig= search&_cdi=6838&_sort=d&_docanchor= &view=c&_ct=1&_acct=C000050221&_version= 1&_urlVersion=0&_userid=10&md5= b96ebda0467adad139ba92827e53789a |
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 |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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_ |
1799132465231560704 |