Ring theoretic aspects of weak Hopf actions
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/25800 |
Resumo: | Following Linchenko and Montgomery's arguments we show that the smash product of a semiprime module algebra, satisfying a polynomial identity and an involutive weak Hopf algebra is semiprime. We get new insight into the existence of non-trivial central invariant elements in non-trivial H-stable ideals of subdirect products of certain H-prime module algebras satisfying a polynomial identity by considering an adapted version of Kaplansky's theorem and by introducing a Brown-McCoy radical for module algebras. We extend Puczylowski and Smoktunowicz's description of the Brown-McCoy radical of a polynomial ring to module algebras and apply our result to left bialgebroid measurings, gradings and involutions. The paper finishes with an extension of results by Bergen et al. and Cohen at al. on irreducible module algebras to weak Hopf actions. |
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Ring theoretic aspects of weak Hopf actionsÁlgebra, MatemáticaAlgebra, MathematicsFollowing Linchenko and Montgomery's arguments we show that the smash product of a semiprime module algebra, satisfying a polynomial identity and an involutive weak Hopf algebra is semiprime. We get new insight into the existence of non-trivial central invariant elements in non-trivial H-stable ideals of subdirect products of certain H-prime module algebras satisfying a polynomial identity by considering an adapted version of Kaplansky's theorem and by introducing a Brown-McCoy radical for module algebras. We extend Puczylowski and Smoktunowicz's description of the Brown-McCoy radical of a polynomial ring to module algebras and apply our result to left bialgebroid measurings, gradings and involutions. The paper finishes with an extension of results by Bergen et al. and Cohen at al. on irreducible module algebras to weak Hopf actions.20092009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/10216/25800engChristian Lompinfo: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:RCAAP2023-11-29T16:09:04Zoai:repositorio-aberto.up.pt:10216/25800Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:38:19.313295Repositório 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 |
Ring theoretic aspects of weak Hopf actions |
title |
Ring theoretic aspects of weak Hopf actions |
spellingShingle |
Ring theoretic aspects of weak Hopf actions Christian Lomp Álgebra, Matemática Algebra, Mathematics |
title_short |
Ring theoretic aspects of weak Hopf actions |
title_full |
Ring theoretic aspects of weak Hopf actions |
title_fullStr |
Ring theoretic aspects of weak Hopf actions |
title_full_unstemmed |
Ring theoretic aspects of weak Hopf actions |
title_sort |
Ring theoretic aspects of weak Hopf actions |
author |
Christian Lomp |
author_facet |
Christian Lomp |
author_role |
author |
dc.contributor.author.fl_str_mv |
Christian Lomp |
dc.subject.por.fl_str_mv |
Álgebra, Matemática Algebra, Mathematics |
topic |
Álgebra, Matemática Algebra, Mathematics |
description |
Following Linchenko and Montgomery's arguments we show that the smash product of a semiprime module algebra, satisfying a polynomial identity and an involutive weak Hopf algebra is semiprime. We get new insight into the existence of non-trivial central invariant elements in non-trivial H-stable ideals of subdirect products of certain H-prime module algebras satisfying a polynomial identity by considering an adapted version of Kaplansky's theorem and by introducing a Brown-McCoy radical for module algebras. We extend Puczylowski and Smoktunowicz's description of the Brown-McCoy radical of a polynomial ring to module algebras and apply our result to left bialgebroid measurings, gradings and involutions. The paper finishes with an extension of results by Bergen et al. and Cohen at al. on irreducible module algebras to weak Hopf actions. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009 2009-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/report |
format |
report |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/10216/25800 |
url |
https://hdl.handle.net/10216/25800 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799136290209267712 |