5 papers · 1 filter
Generalized symmetry in the vanishing of Ext
Tatheer Ajani, Paulo Martins, Victor D. Mendoza Rubio +1
Foundational work by Avramov and Buchweitz, as well as by Huneke and Jorgensen, established symmetry results for the vanishing of Ext over local complete intersections and AB-rings…
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}…
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…