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- Title
Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras.
- Authors
Li, Shen; Marczinzik, René; Zhang, Shunhua
- Abstract
In this article we investigate the relations between the Gorenstein projective dimensions of Λ -modules and their socles for n -minimal Auslander–Gorenstein algebras Λ. First we give a description of projective-injective Λ -modules in terms of their socles. Then we prove that a Λ -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 Λ -module. Furthermore, we show that n -minimal Auslander–Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.
- Subjects
ALGEBRA; DIMENSION theory (Algebra); ARTIN algebras
- Publication
Algebra Colloquium, 2021, Vol 28, Issue 2, p337
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386721000262