English

Indecomposable pure-injective objects in stable categories of Gorenstein-projective modules over Gorenstein orders

Commutative Algebra 2022-10-03 v1 Category Theory Rings and Algebras Representation Theory

Abstract

We give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order is of finite Cohen-Macaulay representation type if and only if every indecomposable pure-injective object in the stable category of Gorenstein-projective modules is compact.

Keywords

Cite

@article{arxiv.2209.15630,
  title  = {Indecomposable pure-injective objects in stable categories of Gorenstein-projective modules over Gorenstein orders},
  author = {Tsutomu Nakamura},
  journal= {arXiv preprint arXiv:2209.15630},
  year   = {2022}
}

Comments

Appendix by Rosanna Laking. 22 pages