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Módulos Totalmente Reflexivos e Dimensão de GorensteinSouza, Thyago Santos de 09 August 2016 (has links)
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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.
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