12 papers
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…
On -finite modules, quasi-injective dimension and width of modules
Victor H. Jorge-Pérez, Paulo Martins
Let be a commutative Noetherian local ring. It is well-known that if is a finitely generated -module of finite quasi-injective dimension, then $\operato…
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…
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}…
Some Homological Conjectures Over Idealization Rings
Igor Nascimento, Victor Jorge-Pérez, Thiago Freitas
Let be a Noetherian local ring and let be a finitely generated -module. The main focus of this paper is to give positive answers for some long-standing…
Hilbert-Kunz Multiplicity of Fiber Product Rings and Nagata Idealizations
Victor H. Jorge-Pérez, Paulo D. C. Martins, J. A. Lima
The main purpose of this paper is to provide formulas for the Hilbert-Kunz multiplicity of fiber product rings and Nagata idealizations. We give explicit formulas for the Hilbert-K…
On Betti numbers for symmetric powers of modules
V. H. Jorge-Pérez, J. A. Lima
Let be a finitely generated module over a local ring . By , we denote the th symmetric power of (th graded component of the symmet…
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…
Mixed multiplicity and Converse of Rees' theorem for modules
M. D. Ferrari, V. H. Jorge-Perez, L. C. Merighe
In this paper, we prove the converse of Rees' mixed multiplicity theorem for modules, which extends the converse of the classical Rees' mixed multiplicity theorem for ideals given…
Rigid modules and homological dimensions
Victor H. Jorge-Pérez, Cleto B. Miranda-Neto
We make use of the concepts of Tor-rigid and rigid-test modules, among others, to investigate the interplay between cohomology vanishing and the finiteness of several homological d…
Generalized local duality, canonical modules, and prescribed bound on projective dimension
Thiago H. Freitas, Victor H. Jorge-Pérez, Cleto B. Miranda-Neto +1
We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well as a general local duality t…