A congruence-free semigroup associated with an infinite cardinal number

Detalhes bibliográficos
Autor(a) principal: Smith, M. Paula Marques
Data de Publicação: 1983
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/11153
Resumo: Let X be a set with infinite cardinality m and let Qm be the semigroup of balanced elements in T (X ), as described by Howie. If I is the ideal {α ∈ Qm : |X α| < m} then the Rees factor Pm = Qm/I is 0 −bisimple and idempotent-generated. Its minimum non-trivial homomorphic image P∗m has both these properties and is congruence-free. Moreover, P∗m has depth 4, in the sense that [E(P∗m)]4 = P∗m and [E(P∗m )]3 ≠ P∗m.
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spelling A congruence-free semigroup associated with an infinite cardinal numberCongruence-freeInfinite cardinalTransformationsIdempotent-generatedLet X be a set with infinite cardinality m and let Qm be the semigroup of balanced elements in T (X ), as described by Howie. If I is the ideal {α ∈ Qm : |X α| < m} then the Rees factor Pm = Qm/I is 0 −bisimple and idempotent-generated. Its minimum non-trivial homomorphic image P∗m has both these properties and is congruence-free. Moreover, P∗m has depth 4, in the sense that [E(P∗m)]4 = P∗m and [E(P∗m )]3 ≠ P∗m.Cambridge University PressUniversidade do MinhoSmith, M. Paula Marques19831983-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/11153eng"Proceedings of the Royal Society of Edinburgh". ISSN 0308-2105. 93A (1983) 245-257.0308-2105info: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:RCAAP2023-12-23T01:29:42Zoai:repositorium.sdum.uminho.pt:1822/11153Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:06:59.776511Repositório 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 A congruence-free semigroup associated with an infinite cardinal number
title A congruence-free semigroup associated with an infinite cardinal number
spellingShingle A congruence-free semigroup associated with an infinite cardinal number
Smith, M. Paula Marques
Congruence-free
Infinite cardinal
Transformations
Idempotent-generated
title_short A congruence-free semigroup associated with an infinite cardinal number
title_full A congruence-free semigroup associated with an infinite cardinal number
title_fullStr A congruence-free semigroup associated with an infinite cardinal number
title_full_unstemmed A congruence-free semigroup associated with an infinite cardinal number
title_sort A congruence-free semigroup associated with an infinite cardinal number
author Smith, M. Paula Marques
author_facet Smith, M. Paula Marques
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Smith, M. Paula Marques
dc.subject.por.fl_str_mv Congruence-free
Infinite cardinal
Transformations
Idempotent-generated
topic Congruence-free
Infinite cardinal
Transformations
Idempotent-generated
description Let X be a set with infinite cardinality m and let Qm be the semigroup of balanced elements in T (X ), as described by Howie. If I is the ideal {α ∈ Qm : |X α| < m} then the Rees factor Pm = Qm/I is 0 −bisimple and idempotent-generated. Its minimum non-trivial homomorphic image P∗m has both these properties and is congruence-free. Moreover, P∗m has depth 4, in the sense that [E(P∗m)]4 = P∗m and [E(P∗m )]3 ≠ P∗m.
publishDate 1983
dc.date.none.fl_str_mv 1983
1983-01-01T00:00:00Z
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 https://hdl.handle.net/1822/11153
url https://hdl.handle.net/1822/11153
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Proceedings of the Royal Society of Edinburgh". ISSN 0308-2105. 93A (1983) 245-257.
0308-2105
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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