发表机构
School of Mathematics and Statistics, Henan University（河南大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对交换Noether环上的模有限代数A，给出n-Gorenstein条件的局部判据，并证明满足Auslander条件时A的自内射维数具有左右对称性。
AI 中文摘要
设A为交换Noether环上的模有限代数，给出A的n-Gorenstein条件的局部判据；作为应用，证明若A满足Auslander条件，则其单侧自内射维数有限可推出另一侧也有限。
英文摘要
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.
Comments12 pages
