Gorenstein Projective Dimensions of Modules over Minimal Auslander-Gorenstein Algebras

• 作者: Shen Li René Marczinzik Shunhua Zhang
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 337-350
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386721000262

摘要

In this article we investigate the relations between the Gorenstein projective dimensions of A-modules and their socles for n-minimal Auslander-Gorenstein algebras A.First we give a description of projective-injective A-modules in terms of their socles.Then we prove that a A-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective A-module.Furthermore,we show that n-minimal Auslander-Gorenstein al-gebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.