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Previous issue date: 2016-08-09 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this dissertation, we study the so-called totally re°exive modules and the notion of Goren-stein dimension over Noetherian commutative rings. The main purpose is to prove the important Auslander-Bridger formula and the Gorenstein theorem, which will allow us to characterize Goren-stein local rings through total re°exivity, as well as to provide su±cient conditions for the property of G-regularity. We furnish, moreover, interesting examples and counterexamples. / Nesta disserta»c~ao, estudamos os chamados m¶odulos totalmente re°exivos e a no»c~ao de dimens~ao
de Gorenstein sobre an¶eis comutativos Noetherianos. A principal ¯nalidade ¶e demonstrar a impor-
tante f¶ormula de Auslander-Bridger e o Teorema de Gorenstein, o que permitir¶a caracterizar an¶eis
locais Gorenstein atrav¶es de re°exividade total, bem como apresentar condi»c~oes su¯cientes para a
propriedade de G-regularidade. Fornecemos, tamb¶em, exemplos e contra-exemplos interessantes.
| Identifer | oai:union.ndltd.org:IBICT/oai:tede.biblioteca.ufpb.br:tede/9266 |
| Date | 09 August 2016 |
| Creators | Souza, Thyago Santos de |
| Contributors | Miranda Neto, Cleto Brasileiro |
| Publisher | Universidade Federal da Paraíba, Programa de Pós-Graduação em Matemática, UFPB, Brasil, Matemática |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFPB, instname:Universidade Federal da Paraíba, instacron:UFPB |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 666657583566969084, 600, 600, 600, 600, -78633126427147401, -7090823417984401694, -2555911436985713659 |
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