Year: 2026
Type: preprint
Abstract: Let $A$ be a module-finite algebra over a commutative Noetherian ring. We give a local criterion for the $n$-Gorenstein condition. For such algebras satisfying the Auslander condition, we prove that finite self-injective dimension is symmetric. Under a one-sided local finiteness hypothesis, we further characterize the Auslander condition by a fiberwise form of Iyama's grade bijection and obtain a criterion for the Auslander--Gorenstein property.
Source: arXiv (Cornell University)
Author: Shen, Dawei
Institution: Henan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203720907