On properties about local cohomology modules, finiteness of torsion and extension functors, and integral closure relative to Artinian modules

• Ano de defesa: 2019
• Autor(a) principal: Merighe, Liliam Carsava
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Álgebra homológica; Attached primes; Cohomologia local generalizada; Fecho integral; Generalized local cohomology; Homological algebra; Integral closure; Multiplicidade; Multiplicity; Primos anexados
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-12082019-101725/

Let R be a non-zero commutative Noetherian ring with unit 1 ≠ 0, a be an ideal of R, and M and N be R-modules. This thesis makes a contribution to the study of generalized local cohomology modules, namely Hia (M;N), with applications for the study of attached primes, torsion product and extension functors, and integral closures and multiplicities relative to Artinian modules. In particular, we obtained results on the following topics: counting the number of non-isomorphic top generalized local cohomology modules, conditions to finiteness, cofiniteness, artinianess and representability of generalized local cohomology modules, torsion product and extension functors applied to R-modules, and conditions to equality between some types of integral closures and multiplicities.