Totally acyclic complexes and locally Gorenstein rings
Commutative Algebra
2017-02-13 v1
Abstract
A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian rings, i.e. we remove the assumption about a dualizing complex. In this context Gorenstein, of course, means locally Gorenstein at every prime.
Cite
@article{arxiv.1702.02986,
title = {Totally acyclic complexes and locally Gorenstein rings},
author = {Lars Winther Christensen and Kiriko Kato},
journal= {arXiv preprint arXiv:1702.02986},
year = {2017}
}
Comments
To appear in J. Algebra Appl.; 5 pp