The ideal structure of nilpotent-generated transformation semigroups
Autor(a) principal: | |
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Data de Publicação: | 1999 |
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/1822/11160 |
Resumo: | In1987 Sullivan determined the elements of the semigroup N (X ) generated by all nilpotent partial transformations of an infinite set X ; later in 1997 he studied subsemigroups of N (X ) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and the Green’s relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X . We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations. |
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The ideal structure of nilpotent-generated transformation semigroupsIdealNilpotent transformationSemigroupCongruencesScience & TechnologyIn1987 Sullivan determined the elements of the semigroup N (X ) generated by all nilpotent partial transformations of an infinite set X ; later in 1997 he studied subsemigroups of N (X ) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and the Green’s relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X . We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.Fundação para a Ciência e a Tecnologia (FCT)Centro de Matemática da Universidade do MinhoCambridge University PressUniversidade do MinhoSmith, M. Paula MarquesSullivan, R. P.19991999-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/11160eng"Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 60 (1999) 303-318.0004-9727info: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:RCAAP2023-07-21T12:36:42Zoai:repositorium.sdum.uminho.pt:1822/11160Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:32:51.186586Repositório 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 |
The ideal structure of nilpotent-generated transformation semigroups |
title |
The ideal structure of nilpotent-generated transformation semigroups |
spellingShingle |
The ideal structure of nilpotent-generated transformation semigroups Smith, M. Paula Marques Ideal Nilpotent transformation Semigroup Congruences Science & Technology |
title_short |
The ideal structure of nilpotent-generated transformation semigroups |
title_full |
The ideal structure of nilpotent-generated transformation semigroups |
title_fullStr |
The ideal structure of nilpotent-generated transformation semigroups |
title_full_unstemmed |
The ideal structure of nilpotent-generated transformation semigroups |
title_sort |
The ideal structure of nilpotent-generated transformation semigroups |
author |
Smith, M. Paula Marques |
author_facet |
Smith, M. Paula Marques Sullivan, R. P. |
author_role |
author |
author2 |
Sullivan, R. P. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Smith, M. Paula Marques Sullivan, R. P. |
dc.subject.por.fl_str_mv |
Ideal Nilpotent transformation Semigroup Congruences Science & Technology |
topic |
Ideal Nilpotent transformation Semigroup Congruences Science & Technology |
description |
In1987 Sullivan determined the elements of the semigroup N (X ) generated by all nilpotent partial transformations of an infinite set X ; later in 1997 he studied subsemigroups of N (X ) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and the Green’s relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X . We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations. |
publishDate |
1999 |
dc.date.none.fl_str_mv |
1999 1999-01-01T00:00:00Z |
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/1822/11160 |
url |
http://hdl.handle.net/1822/11160 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"Bulletin of the Australian Mathematical Society". ISSN 0004-9727. 60 (1999) 303-318. 0004-9727 |
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 |
Cambridge University Press |
publisher.none.fl_str_mv |
Cambridge University Press |
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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1799132843266277376 |