| Texto completo | |
| Autor(es): |
Jorge-Perez, Victor H.
;
Martins, Paulo
;
Mendoza-Rubio, Victor D.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Algebra; v. 690, p. 24-pg., 2026-03-15. |
| Resumo | |
The quasi-projective dimension and quasi-injective dimension are recently introduced homological invariants that generalize the classical notions of projective dimension and injective dimension, respectively. For a local ring Rand finitely generated R-modules M and N, we provide conditions involving quasi-homological dimensions where the equality sup{i >= 0 : Ext(R)(i)(M, N) not equal 0} = depth R-depth M, which we call Ischebeck's formula, holds. One of the results in this direction generalizes a well-known result of Ischebeck concerning modules of finite injective dimension, considering the quasi-injective dimension. On the other hand, we establish an inequality relating the quasi-projective dimension of a finitely generated module to its grade and introduce the concept of a quasi-perfect module as a natural generalization of a perfect module. We prove some results for this new concept similar to the classical results. Additionally, we provide a formula for the grade of finitely generated modules with finite quasi-injective dimension over a local ring, as well as grade inequalities for modules of finite quasi-projective dimension. In our study, Cohen-Macaulayness criteria are also obtained. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| 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 |
| Processo FAPESP: | 23/15733-5 - Anulamento de Ext e Tor, e módulos livres |
| Beneficiário: | Victor Daniel Mendoza Rubio |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |
| Processo FAPESP: | 22/03372-5 - Sobre a conjectura de Auslander-Reiten |
| Beneficiário: | Victor Daniel Mendoza Rubio |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |
| Processo FAPESP: | 19/21181-0 - Novas fronteiras na Teoria de Singularidades |
| Beneficiário: | Regilene Delazari dos Santos Oliveira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |