Sobre ideais primos anexados de módulos

• Ano de defesa: 2016
• Autor(a) principal: Menezes, Clemerson Oliveira da Silva
• Tipo de documento: Dissertação
• 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: Representação secundária; Primos anexados; Dualidade de Matlis; Co-localização; Cohomologia local; Secondary representation; Atached primes; Matlis duality; Co-localisation; Local cohomology; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9240

The connection between the theory of local cohomology and the theory of secondary representation and attached prime ideals is exposed in the work of R. Y. Sharp and I. G. Macdonald and it displayed itself as very prolific since the statement of various conditions of vanishing and non-vanishing for some local cohomology modules. In this work we show that, in some conditions, the (generalised) Matlis dual DR (M ) of a module M over a semi-local ring R is Artinian, hence representable. Under the same conditions we show that AttR (DR (M )) = Ass(M ). We also describe the set of attached primes of co-localisations of modules and of some local cohomology modules. The use for the latter is, as an example, to describe the set of attached primes of the top local cohomology module Ha dim(R)(R) as the set of prime ideals of R which satisfy the condition of Lichtenbaum–Hartshorne Vanishing Theorem.