Definable subcategories and the ziegler spectrum

Detalhes bibliográficos
Ano de defesa: 2019
Autor(a) principal: João Vitor Pinto e Silva
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Minas Gerais
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Matemática - Teses
Álgebra - teses
Teoria de módulos
Anéis associativos
Link de acesso: https://hdl.handle.net/1843/32083
Resumo: In (ZIEGLER, 1984) Ziegler associated a topological space to the category of modules over any associative ring with unit. This space, now known as the Ziegler Spectrum, has as points the isomorphism classes of pure-injective indecomposable modules. This topological space is able to give a better understanding to the category of modules. The main objective of this text is to give some necessary definitions to understand the Ziegler spectrum and proof some important results about it. The focus of the text are definable subcategories of Mod-R, defining the Ziegler spectrum, proof some results related to it and give the example of the Ziegler Spectrum for discrete valuation rings.
id UFMG_3240907f2b679ea20f4f8b751a6bc1c7
oai_identifier_str oai:repositorio.ufmg.br:1843/32083
network_acronym_str UFMG
network_name_str Repositório Institucional da UFMG
repository_id_str
spelling 2020-01-21T14:47:39Z2025-09-09T01:08:40Z2020-01-21T14:47:39Z2019-06-25https://hdl.handle.net/1843/32083In (ZIEGLER, 1984) Ziegler associated a topological space to the category of modules over any associative ring with unit. This space, now known as the Ziegler Spectrum, has as points the isomorphism classes of pure-injective indecomposable modules. This topological space is able to give a better understanding to the category of modules. The main objective of this text is to give some necessary definitions to understand the Ziegler spectrum and proof some important results about it. The focus of the text are definable subcategories of Mod-R, defining the Ziegler spectrum, proof some results related to it and give the example of the Ziegler Spectrum for discrete valuation rings.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoporUniversidade Federal de Minas Geraishttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/info:eu-repo/semantics/openAccessAlgebraTeoria de módulosTeoria de modelosEspectro de ZieglerSubcategorias definíveis.Matemática - TesesÁlgebra - tesesTeoria de módulosAnéis associativosDefinable subcategories and the ziegler spectruminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisJoão Vitor Pinto e Silvareponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGhttp://lattes.cnpq.br/7931559004112832John William MacQuarriehttp://lattes.cnpq.br/7878226069423105Csaba SchneiderLucas Henrique CalixtoEm (ZIEGLER, 1984) Ziegler associou um espaço topológico a categoria de módulos sobre qualquer anel associativo com unidade. Esse espaço, agora conhecido como Espectro de Ziegler, tem como pontos as classes de isomorfismos dos módulos puro-injetivos indecomponíveis. Este espaço topológico serve para o melhor entendimento da categoria de módulos. O objetivo deste texto é dar algumas definições necessárias para o entendimento do Espectro de Ziegler e demonstrar resultados importantes sobre elas. Os principais focos do texto são falar sobre subcategorias definíveis de Mod-R, definir o Espectro de Ziegler, demonstrar resultados relacionados a ele e dar o exemplo do Espectro de Ziegler para anéis de valuação discreta.BrasilICX - DEPARTAMENTO DE MATEMÁTICAPrograma de Pós-Graduação em MatemáticaUFMGORIGINALDiss326.pdfapplication/pdf683975https://repositorio.ufmg.br//bitstreams/3fff1393-216c-4c06-8e69-497a773916cf/download24c0ddd78e0316f9f234280ee8fa89d9MD51trueAnonymousREADCC-LICENSElicense_rdfapplication/octet-stream811https://repositorio.ufmg.br//bitstreams/9cf9e6a1-419b-450f-8c88-a1ce5f46b250/downloadcfd6801dba008cb6adbd9838b81582abMD52falseAnonymousREADLICENSElicense.txttext/plain2119https://repositorio.ufmg.br//bitstreams/cdb52321-0dfe-4936-b5cd-cf6f40dbf7d0/download34badce4be7e31e3adb4575ae96af679MD53falseAnonymousREADTEXTDiss326.pdf.txttext/plain134875https://repositorio.ufmg.br//bitstreams/4d946e26-c2cb-4de6-9a09-24816fd30e5a/download2012ff38101d90ead7228f27a54db0bfMD54falseAnonymousREAD1843/320832025-09-08 22:08:40.963http://creativecommons.org/licenses/by-nc-nd/3.0/pt/Acesso Abertoopen.accessoai:repositorio.ufmg.br:1843/32083https://repositorio.ufmg.br/Repositório InstitucionalPUBhttps://repositorio.ufmg.br/oairepositorio@ufmg.bropendoar:2025-09-09T01:08:40Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)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
dc.title.none.fl_str_mv Definable subcategories and the ziegler spectrum
title Definable subcategories and the ziegler spectrum
spellingShingle Definable subcategories and the ziegler spectrum
João Vitor Pinto e Silva
Matemática - Teses
Álgebra - teses
Teoria de módulos
Anéis associativos
Algebra
Teoria de módulos
Teoria de modelos
Espectro de Ziegler
Subcategorias definíveis.
title_short Definable subcategories and the ziegler spectrum
title_full Definable subcategories and the ziegler spectrum
title_fullStr Definable subcategories and the ziegler spectrum
title_full_unstemmed Definable subcategories and the ziegler spectrum
title_sort Definable subcategories and the ziegler spectrum
author João Vitor Pinto e Silva
author_facet João Vitor Pinto e Silva
author_role author
dc.contributor.author.fl_str_mv João Vitor Pinto e Silva
dc.subject.por.fl_str_mv Matemática - Teses
Álgebra - teses
Teoria de módulos
Anéis associativos
topic Matemática - Teses
Álgebra - teses
Teoria de módulos
Anéis associativos
Algebra
Teoria de módulos
Teoria de modelos
Espectro de Ziegler
Subcategorias definíveis.
dc.subject.other.none.fl_str_mv Algebra
Teoria de módulos
Teoria de modelos
Espectro de Ziegler
Subcategorias definíveis.
description In (ZIEGLER, 1984) Ziegler associated a topological space to the category of modules over any associative ring with unit. This space, now known as the Ziegler Spectrum, has as points the isomorphism classes of pure-injective indecomposable modules. This topological space is able to give a better understanding to the category of modules. The main objective of this text is to give some necessary definitions to understand the Ziegler spectrum and proof some important results about it. The focus of the text are definable subcategories of Mod-R, defining the Ziegler spectrum, proof some results related to it and give the example of the Ziegler Spectrum for discrete valuation rings.
publishDate 2019
dc.date.issued.fl_str_mv 2019-06-25
dc.date.accessioned.fl_str_mv 2020-01-21T14:47:39Z
2025-09-09T01:08:40Z
dc.date.available.fl_str_mv 2020-01-21T14:47:39Z
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.uri.fl_str_mv https://hdl.handle.net/1843/32083
url https://hdl.handle.net/1843/32083
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/3.0/pt/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/3.0/pt/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
instname_str Universidade Federal de Minas Gerais (UFMG)
instacron_str UFMG
institution UFMG
reponame_str Repositório Institucional da UFMG
collection Repositório Institucional da UFMG
bitstream.url.fl_str_mv https://repositorio.ufmg.br//bitstreams/3fff1393-216c-4c06-8e69-497a773916cf/download
https://repositorio.ufmg.br//bitstreams/9cf9e6a1-419b-450f-8c88-a1ce5f46b250/download
https://repositorio.ufmg.br//bitstreams/cdb52321-0dfe-4936-b5cd-cf6f40dbf7d0/download
https://repositorio.ufmg.br//bitstreams/4d946e26-c2cb-4de6-9a09-24816fd30e5a/download
bitstream.checksum.fl_str_mv 24c0ddd78e0316f9f234280ee8fa89d9
cfd6801dba008cb6adbd9838b81582ab
34badce4be7e31e3adb4575ae96af679
2012ff38101d90ead7228f27a54db0bf
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)
repository.mail.fl_str_mv repositorio@ufmg.br
_version_ 1862105890447949824

Registros relacionados