5 papers
Remarks on Auslander's depth formula for quasi-projective dimension
Victor H. Jorge-Pérez, Paulo Martins, Victor D. Mendoza-Rubio
For nonzero finitely generated -modules and over a Noetherian local ring , Auslander's depth formula is the equality $$ \operatorname{depth} M + \operatorname{depth}…
On Extension modules of finite homological dimension
Rafael Holanda, Victor H. Jorge-Pérez, Victor D. Mendoza-Rubio
We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In…
Ischebeck's formula, grade and quasi-homological dimensions
Victor H. Jorge-Pérez, Paulo Martins, Victor D. Mendoza-Rubio
The quasi-projective dimension and quasi-injective dimension are recently introduced homological invariants that generalize the classical notions of projective dimension and inject…
On modules whose dual is of finite Gorenstein dimension
Victor D. Mendoza-Rubio, Victor H. Jorge-Pérez
In this paper, we aim to obtain some results under the condition that the dual of a module over a commutative Noetherian ring has finite Gorenstein dimension. In this direction, we…
The Auslander-Reiten Conjecture, Finite -Injective Dimension of , and vanishing of
Victor D. Mendoza-Rubio, Victor H. Jorge-Pérez
Let be a Noetherian local ring, and let be a semidualizing -module. In this paper, we present some results concerning the vanishing of and finite in…