A nilpotent generated semigroup associated with a semigroup of full transformations
Autor(a) principal: | |
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Data de Publicação: | 1988 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/14506 |
Resumo: | Let $X$ be a set with infinite regular cardinality $m$ and let $\mathcal T(X)$ be the semigroup of all self-maps of $X$. The semigroup $Q_m$ of ‘balanced’ elements of $\mathcal T(X)$ plays an important role in the study by Howie [3,5,6] of idempotent-generated subsemigroups of $\mathcal T(X)$, as does the subset $S_m$ of ‘stable’ elements, which is a subsemigroup of $Q_m$ if and only if $m$ is a regular cardinal. The principal factor $P_m$ of $Q_m$, corresponding to the maximum $\mathcal J$-class $J_m$, contains $S_m$ and has been shown in [7] to have a number of interesting properties. Let $N_2$ be the set of all nilpotent elements of index 2 in $P_m$. Then the subsemigroup $<N_2>$ of $P_m$ generated by $N_2$ consists exactly of the elements in $P_m\backslash S_m$. Moreover $P_m\backslash S_m$ has 2-nilpotent-depth 3, in the sense that $N_2\cup N_2^2 \subset P_m\backslash S_m=N_2 \cup N_2^2\cup N_2^3$. |
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A nilpotent generated semigroup associated with a semigroup of full transformationsSemigroupNilpotentsTransformationsCardinalScience & TechnologyLet $X$ be a set with infinite regular cardinality $m$ and let $\mathcal T(X)$ be the semigroup of all self-maps of $X$. The semigroup $Q_m$ of ‘balanced’ elements of $\mathcal T(X)$ plays an important role in the study by Howie [3,5,6] of idempotent-generated subsemigroups of $\mathcal T(X)$, as does the subset $S_m$ of ‘stable’ elements, which is a subsemigroup of $Q_m$ if and only if $m$ is a regular cardinal. The principal factor $P_m$ of $Q_m$, corresponding to the maximum $\mathcal J$-class $J_m$, contains $S_m$ and has been shown in [7] to have a number of interesting properties. Let $N_2$ be the set of all nilpotent elements of index 2 in $P_m$. Then the subsemigroup $<N_2>$ of $P_m$ generated by $N_2$ consists exactly of the elements in $P_m\backslash S_m$. Moreover $P_m\backslash S_m$ has 2-nilpotent-depth 3, in the sense that $N_2\cup N_2^2 \subset P_m\backslash S_m=N_2 \cup N_2^2\cup N_2^3$.Cambridge University PressUniversidade do MinhoHowie, John M.Smith, M. Paula Marques19881988-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/14506eng0308-210510.1017/S0308210500026615info: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:RCAAP2023-12-23T01:31:33Zoai:repositorium.sdum.uminho.pt:1822/14506Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:21:11.774834Repositório 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 nilpotent generated semigroup associated with a semigroup of full transformations |
title |
A nilpotent generated semigroup associated with a semigroup of full transformations |
spellingShingle |
A nilpotent generated semigroup associated with a semigroup of full transformations Howie, John M. Semigroup Nilpotents Transformations Cardinal Science & Technology |
title_short |
A nilpotent generated semigroup associated with a semigroup of full transformations |
title_full |
A nilpotent generated semigroup associated with a semigroup of full transformations |
title_fullStr |
A nilpotent generated semigroup associated with a semigroup of full transformations |
title_full_unstemmed |
A nilpotent generated semigroup associated with a semigroup of full transformations |
title_sort |
A nilpotent generated semigroup associated with a semigroup of full transformations |
author |
Howie, John M. |
author_facet |
Howie, John M. Smith, M. Paula Marques |
author_role |
author |
author2 |
Smith, M. Paula Marques |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Howie, John M. Smith, M. Paula Marques |
dc.subject.por.fl_str_mv |
Semigroup Nilpotents Transformations Cardinal Science & Technology |
topic |
Semigroup Nilpotents Transformations Cardinal Science & Technology |
description |
Let $X$ be a set with infinite regular cardinality $m$ and let $\mathcal T(X)$ be the semigroup of all self-maps of $X$. The semigroup $Q_m$ of ‘balanced’ elements of $\mathcal T(X)$ plays an important role in the study by Howie [3,5,6] of idempotent-generated subsemigroups of $\mathcal T(X)$, as does the subset $S_m$ of ‘stable’ elements, which is a subsemigroup of $Q_m$ if and only if $m$ is a regular cardinal. The principal factor $P_m$ of $Q_m$, corresponding to the maximum $\mathcal J$-class $J_m$, contains $S_m$ and has been shown in [7] to have a number of interesting properties. Let $N_2$ be the set of all nilpotent elements of index 2 in $P_m$. Then the subsemigroup $<N_2>$ of $P_m$ generated by $N_2$ consists exactly of the elements in $P_m\backslash S_m$. Moreover $P_m\backslash S_m$ has 2-nilpotent-depth 3, in the sense that $N_2\cup N_2^2 \subset P_m\backslash S_m=N_2 \cup N_2^2\cup N_2^3$. |
publishDate |
1988 |
dc.date.none.fl_str_mv |
1988 1988-01-01T00:00:00Z |
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/1822/14506 |
url |
https://hdl.handle.net/1822/14506 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0308-2105 10.1017/S0308210500026615 |
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 |
repository.mail.fl_str_mv |
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1799132677474877440 |