Indecomposable pure-injective objects in stable categories of Gorenstein-projective modules over Gorenstein orders
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2022
- DOI:
- 10.48550/arXiv.2209.15630
- arXiv:
- arXiv:2209.15630
- Bibcode:
- 2022arXiv220915630N
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Category Theory;
- Mathematics - Rings and Algebras;
- Mathematics - Representation Theory;
- 13C14;
- 16G30 (Primary);
- 13H10;
- 16D40;
- 16G60;
- 16D70 (Secondary)
- E-Print:
- Appendix by Rosanna Laking. 22 pages