• DOI:10.1142/S1005386721000262
• Corpus ID: 55944287

Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras

@article{Li2018GorensteinPD,
  title={Gorenstein Projective Dimensions of Modules over Minimal Auslander–Gorenstein Algebras},
  author={Shen Li and Ren{\'e} Marczinzik and Shunhua Zhang},
  journal={Algebra Colloquium},
  year={2018}
}

• Shen Li, René Marczinzik, Shunhua Zhang
• Published 1 February 2018
• Mathematics
• Algebra Colloquium

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