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math.AC2024
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…
math.AC2024
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}…
math.AC2024
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…