Uma jornada aos anéis de Gorenstein

Detalhes bibliográficos
Autor(a) principal: Dosea, André Santana
Data de Publicação: 2019
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFS
Texto Completo: http://ri.ufs.br/jspui/handle/riufs/16246
Resumo: This work has as main goal to make a detailed study of Gorenstein rings and your role in local duality theory. At the beginning, some pre-requisites are studied like the Krull dimension of modules, Koszul Complexes and Cohen-Macaulay rings. Concerning to this last topic, we studied in more detail the regular rings and the complete intersection rings. We showed that all this rings are Gorenstein. Also, we present the characterization of Gorenstein rings in terms of the concept of type of a ring. Ultimately, we present the concept of canonical module, highlighting your role in Local Duality Theory over maximal Cohen-Macaulay modules.
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spelling Dosea, André SantanaRamos, Zaqueu Alves2022-09-02T17:01:37Z2022-09-02T17:01:37Z2019-02-28DOSEA, André Santana. Uma jornada aos anéis de Gorenstein. 2019. 179 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2019.http://ri.ufs.br/jspui/handle/riufs/16246This work has as main goal to make a detailed study of Gorenstein rings and your role in local duality theory. At the beginning, some pre-requisites are studied like the Krull dimension of modules, Koszul Complexes and Cohen-Macaulay rings. Concerning to this last topic, we studied in more detail the regular rings and the complete intersection rings. We showed that all this rings are Gorenstein. Also, we present the characterization of Gorenstein rings in terms of the concept of type of a ring. Ultimately, we present the concept of canonical module, highlighting your role in Local Duality Theory over maximal Cohen-Macaulay modules.Esta dissertação tem como objetivo principal fazer um estudo detalhado dos anéis de Gorenstein e seu papel na teoria de dualidade local. Iniciamos estudando alguns pré-requisitos como dimensão de krull de módulos, complexos de Koszul e anéis Cohen-Macaulay. Neste último tópico, estudamos com mais detalhes os anéis regulares e de interseção completa. Mostramos que todos estes anéis são Gorenstein. Caracterizamos os anéis de Gorenstein a partir do conceito de tipo de anel. Por fim, estudamos o modulo canônico, destacando seu papel na teoria de dualidade local sobre anéis Cohen-Macaulay máximos.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão CristóvãoporMatemáticaÁlgebraHomologiaAnéis de GorensteinMódulo canônicoGorenstein ringsHomologyCanonical moduleCIENCIAS EXATAS E DA TERRA::MATEMATICAUma jornada aos anéis de Gorensteininfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPós-Graduação em MatemáticaUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessORIGINALANDRE_SANTANA_DOSEA.pdfANDRE_SANTANA_DOSEA.pdfapplication/pdf1251018https://ri.ufs.br/jspui/bitstream/riufs/16246/2/ANDRE_SANTANA_DOSEA.pdfc45b5268ef44e93da82a5a6092c124ebMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/16246/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51TEXTANDRE_SANTANA_DOSEA.pdf.txtANDRE_SANTANA_DOSEA.pdf.txtExtracted texttext/plain295959https://ri.ufs.br/jspui/bitstream/riufs/16246/3/ANDRE_SANTANA_DOSEA.pdf.txt6201ec7283fa825b1270d158598ab1dbMD53THUMBNAILANDRE_SANTANA_DOSEA.pdf.jpgANDRE_SANTANA_DOSEA.pdf.jpgGenerated Thumbnailimage/jpeg1425https://ri.ufs.br/jspui/bitstream/riufs/16246/4/ANDRE_SANTANA_DOSEA.pdf.jpg3545c100fe066376d8d54a06dadfb734MD54riufs/162462022-09-02 14:01:38.074oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2022-09-02T17:01:38Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Uma jornada aos anéis de Gorenstein
title Uma jornada aos anéis de Gorenstein
spellingShingle Uma jornada aos anéis de Gorenstein
Dosea, André Santana
Matemática
Álgebra
Homologia
Anéis de Gorenstein
Módulo canônico
Gorenstein rings
Homology
Canonical module
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Uma jornada aos anéis de Gorenstein
title_full Uma jornada aos anéis de Gorenstein
title_fullStr Uma jornada aos anéis de Gorenstein
title_full_unstemmed Uma jornada aos anéis de Gorenstein
title_sort Uma jornada aos anéis de Gorenstein
author Dosea, André Santana
author_facet Dosea, André Santana
author_role author
dc.contributor.author.fl_str_mv Dosea, André Santana
dc.contributor.advisor1.fl_str_mv Ramos, Zaqueu Alves
contributor_str_mv Ramos, Zaqueu Alves
dc.subject.por.fl_str_mv Matemática
Álgebra
Homologia
Anéis de Gorenstein
Módulo canônico
topic Matemática
Álgebra
Homologia
Anéis de Gorenstein
Módulo canônico
Gorenstein rings
Homology
Canonical module
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Gorenstein rings
Homology
Canonical module
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description This work has as main goal to make a detailed study of Gorenstein rings and your role in local duality theory. At the beginning, some pre-requisites are studied like the Krull dimension of modules, Koszul Complexes and Cohen-Macaulay rings. Concerning to this last topic, we studied in more detail the regular rings and the complete intersection rings. We showed that all this rings are Gorenstein. Also, we present the characterization of Gorenstein rings in terms of the concept of type of a ring. Ultimately, we present the concept of canonical module, highlighting your role in Local Duality Theory over maximal Cohen-Macaulay modules.
publishDate 2019
dc.date.issued.fl_str_mv 2019-02-28
dc.date.accessioned.fl_str_mv 2022-09-02T17:01:37Z
dc.date.available.fl_str_mv 2022-09-02T17:01:37Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv DOSEA, André Santana. Uma jornada aos anéis de Gorenstein. 2019. 179 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2019.
dc.identifier.uri.fl_str_mv http://ri.ufs.br/jspui/handle/riufs/16246
identifier_str_mv DOSEA, André Santana. Uma jornada aos anéis de Gorenstein. 2019. 179 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2019.
url http://ri.ufs.br/jspui/handle/riufs/16246
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.program.fl_str_mv Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFS
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
instname_str Universidade Federal de Sergipe (UFS)
instacron_str UFS
institution UFS
reponame_str Repositório Institucional da UFS
collection Repositório Institucional da UFS
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