Idempotent Submodules
Autor(a) principal: | |
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Data de Publicação: | 2006 |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/25795 |
Resumo: | Bican, Jambor, Kepka and Nemec defined a product on the lattice of submodules of a module, making any module into a partially ordered groupoid. Submodules that are idempotent with respect to this product behave similar as idempotent ideals in rings. In particular jansian torsion theories can be described through idempotent submodules. Moreover so-called coclosed submodules, which are essentially closed elements in the dual lattice of submodules of a module, turn out to be idempotent in pi-projective modules. The relation of strongly copolyform modules and the regularity of their endomorphism ring is discussed. |
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Idempotent SubmodulesÁlgebra, MatemáticaAlgebra, MathematicsBican, Jambor, Kepka and Nemec defined a product on the lattice of submodules of a module, making any module into a partially ordered groupoid. Submodules that are idempotent with respect to this product behave similar as idempotent ideals in rings. In particular jansian torsion theories can be described through idempotent submodules. Moreover so-called coclosed submodules, which are essentially closed elements in the dual lattice of submodules of a module, turn out to be idempotent in pi-projective modules. The relation of strongly copolyform modules and the regularity of their endomorphism ring is discussed.20062006-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/10216/25795engChristian 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:RCAAP2023-11-29T13:32:14Zoai:repositorio-aberto.up.pt:10216/25795Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:42:09.846517Repositório 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 |
Idempotent Submodules |
title |
Idempotent Submodules |
spellingShingle |
Idempotent Submodules Christian Lomp Álgebra, Matemática Algebra, Mathematics |
title_short |
Idempotent Submodules |
title_full |
Idempotent Submodules |
title_fullStr |
Idempotent Submodules |
title_full_unstemmed |
Idempotent Submodules |
title_sort |
Idempotent Submodules |
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 |
Bican, Jambor, Kepka and Nemec defined a product on the lattice of submodules of a module, making any module into a partially ordered groupoid. Submodules that are idempotent with respect to this product behave similar as idempotent ideals in rings. In particular jansian torsion theories can be described through idempotent submodules. Moreover so-called coclosed submodules, which are essentially closed elements in the dual lattice of submodules of a module, turn out to be idempotent in pi-projective modules. The relation of strongly copolyform modules and the regularity of their endomorphism ring is discussed. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006 2006-01-01T00:00:00Z |
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/10216/25795 |
url |
https://hdl.handle.net/10216/25795 |
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 |
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 |
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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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1799135736552751105 |