On topological lattices and their applications to module theory

Bibliographic Details
Main Author: Abuhlail, J
Publication Date: 2016
Other Authors: Christian Lomp
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/10216/90083
Summary: Yassemi's "second submodules" are dualized and properties of its spectrum are studied. This is done by moving the ring theoretical setting to a lattice theoretical one and by introducing the notion of a (strongly) topological lattice L = (L, Lambda, V) with respect to a proper subset X of L. We investigate and characterize (strongly) topological lattices in general in order to apply it to modules over associative unital rings. Given a non-zero left R-module M, we introduce and investigate the spectrum Spec(f) (M) of first submodules of M as a dual notion of Yassemi's second submodules. We topologize Spec(f) (M) and investigate the algebraic properties of M by passing to the topological properties of the associated space.
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spelling On topological lattices and their applications to module theoryÁlgebra, MatemáticaAlgebra, MathematicsYassemi's "second submodules" are dualized and properties of its spectrum are studied. This is done by moving the ring theoretical setting to a lattice theoretical one and by introducing the notion of a (strongly) topological lattice L = (L, Lambda, V) with respect to a proper subset X of L. We investigate and characterize (strongly) topological lattices in general in order to apply it to modules over associative unital rings. Given a non-zero left R-module M, we introduce and investigate the spectrum Spec(f) (M) of first submodules of M as a dual notion of Yassemi's second submodules. We topologize Spec(f) (M) and investigate the algebraic properties of M by passing to the topological properties of the associated space.20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/90083eng0219-498810.1142/s0219498816500468Abuhlail, JChristian 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:RCAAP2025-02-27T17:29:27Zoai:repositorio-aberto.up.pt:10216/90083Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T22:16:12.084645Repositórios 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 On topological lattices and their applications to module theory
title On topological lattices and their applications to module theory
spellingShingle On topological lattices and their applications to module theory
Abuhlail, J
Álgebra, Matemática
Algebra, Mathematics
title_short On topological lattices and their applications to module theory
title_full On topological lattices and their applications to module theory
title_fullStr On topological lattices and their applications to module theory
title_full_unstemmed On topological lattices and their applications to module theory
title_sort On topological lattices and their applications to module theory
author Abuhlail, J
author_facet Abuhlail, J
Christian Lomp
author_role author
author2 Christian Lomp
author2_role author
dc.contributor.author.fl_str_mv Abuhlail, J
Christian Lomp
dc.subject.por.fl_str_mv Álgebra, Matemática
Algebra, Mathematics
topic Álgebra, Matemática
Algebra, Mathematics
description Yassemi's "second submodules" are dualized and properties of its spectrum are studied. This is done by moving the ring theoretical setting to a lattice theoretical one and by introducing the notion of a (strongly) topological lattice L = (L, Lambda, V) with respect to a proper subset X of L. We investigate and characterize (strongly) topological lattices in general in order to apply it to modules over associative unital rings. Given a non-zero left R-module M, we introduce and investigate the spectrum Spec(f) (M) of first submodules of M as a dual notion of Yassemi's second submodules. We topologize Spec(f) (M) and investigate the algebraic properties of M by passing to the topological properties of the associated space.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
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/10216/90083
url https://hdl.handle.net/10216/90083
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0219-4988
10.1142/s0219498816500468
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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