5 papers · 1 filter
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…