On the theory of Gorenstein dimension with respect to a semidualizing module

• Ano de defesa: 2019
• Autor(a) principal: Souza, Thyago Santos de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Dimensão de Gorenstein; Módulo semidualizante; Transposta de Auslander; Módulo torsionless; Módulo horizontalmente ligado; Módulo de derivações; Gorenstein dimension; Semidualizing module; Auslander transpose; Torsionless module; Horizontally linked module; Derivation module; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/17050

This work studies the notions of k-torsionless modules and reduced G-perfect modules in a more general setting, relative to a semidualizing module. We consider various aspects and obtain new characterizations of these properties, which led us to generalize previous results by several authors. As a special application, we investigate the CohenMacaulayness, under certain conditions, on a celebrated module in both algebra and geometry: the module of derivations. Finally, the intersection of the two main general classes of modules worked out in this thesis is taken into account and exemplified.