| Texto completo | |
| Autor(es): |
Jorge-Perez, V. H.
;
Martins, Paulo
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | COMMUNICATIONS IN ALGEBRA; v. N/A, p. 9-pg., 2025-12-06. |
| Resumo | |
Let (R,m,k) be a commutative Noetherian local ring. It is well-known that if M is a finitely generated R-module of finite quasi-injective dimension, then qid(R)M=depth R. In this paper, we demonstrate that under the weaker condition that M is Ext-finite and has finite quasi-injective dimension, the equality qid(R)M=0 holds if and only if Ext(R)(i)>0(R/(x),M)=0, where x is an element of m is a maximal R-sequence and if qid(R)M not equal 0, we show then that qid(R)M=sup{i:Ext(R)(i)(R/(x),M)not equal 0}. Also, we show that if R is a Cohen-Macaulay local ring and M is an Ext-finite R-module of finite quasi-injective dimension, then depth R=qid(R)M+inf{i:Tor(i)(R)(k,M)not equal 0}, provided that inf{i:Tor(i)(R)(k,M)not equal 0}<infinity. (AU) | |
| Processo FAPESP: | 19/21181-0 - Novas fronteiras na Teoria de Singularidades |
| Beneficiário: | Regilene Delazari dos Santos Oliveira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 22/12114-0 - Os funtores Tor e Ext: propriedades de anulamento e problemas relacionados |
| Beneficiário: | Paulo Damião Christo Martins |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |