PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/25782 |
Resumo: | Primeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules (M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which (M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz' "weakly compressible" modules. In particular we are interested in representing weakly compressible modules as a subdirect product of "prime" modules in a suitable sense. It turns out that any weakly compressible module is a subdirect product of prime modules (in the sense of Kaplansky). Moreover if M is a self-projective module, then M is weakly compressible if and only if it is a subdirect product of prime modules (in the sense of Bican et al.). An application to Hopf actions is given. |
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PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONSÁlgebra, MatemáticaAlgebra, MathematicsPrimeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules (M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which (M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz' "weakly compressible" modules. In particular we are interested in representing weakly compressible modules as a subdirect product of "prime" modules in a suitable sense. It turns out that any weakly compressible module is a subdirect product of prime modules (in the sense of Kaplansky). Moreover if M is a self-projective module, then M is weakly compressible if and only if it is a subdirect product of prime modules (in the sense of Bican et al.). An application to Hopf actions is given.20052005-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/25782eng0219-498810.1142/s0219498805001022Christian 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:RCAAP2023-11-29T12:53:55Zoai:repositorio-aberto.up.pt:10216/25782Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:28:56.748630Repositório 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 |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS |
title |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS |
spellingShingle |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS Christian Lomp Álgebra, Matemática Algebra, Mathematics |
title_short |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS |
title_full |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS |
title_fullStr |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS |
title_full_unstemmed |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS |
title_sort |
PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA 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 |
Primeness on modules can be defined by prime elements in a suitable partially ordered groupoid. Using a product on the lattice of submodules (M) of a module M defined in [3] we revise the concept of prime modules in this sense. Those modules M for which (M) has no nilpotent elements have been studied by Jirasko and they coincide with Zelmanowitz' "weakly compressible" modules. In particular we are interested in representing weakly compressible modules as a subdirect product of "prime" modules in a suitable sense. It turns out that any weakly compressible module is a subdirect product of prime modules (in the sense of Kaplansky). Moreover if M is a self-projective module, then M is weakly compressible if and only if it is a subdirect product of prime modules (in the sense of Bican et al.). An application to Hopf actions is given. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005 2005-01-01T00:00:00Z |
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/10216/25782 |
url |
https://hdl.handle.net/10216/25782 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0219-4988 10.1142/s0219498805001022 |
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.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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1799135596930662400 |