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