Idempotent Submodules

Bibliographic Details
Main Author: Christian Lomp
Publication Date: 2006
Format: Report
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/10216/25795
Summary: 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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spelling 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-02-27T17:47:03Zoai:repositorio-aberto.up.pt:10216/25795Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T22:26:28.546287Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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
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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
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dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
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collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
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