Some characterizations of local rings via reducing dimensions
Abstract
In this paper, we study homological dimensions of finitely generated modules over commutative Noetherian local rings called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings via reducing homological dimensions. For example, we extend a classical result of Auslander and Bridger and prove that a local ring is Gorenstein if and only if each finitely generated module over it has a finite reducing Gorenstein dimension. Along the way, we prove various connections between complexity and the reducing projective dimension of modules.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Kyoto journal of mathematics
- Publisher
- Duke University Press
- Volume
- -1
- Issue
- -1
- Pages
- 1–28
- Publication date
- 1 January 2026
- Language
- EN