Homological dimensions of complexes over coherent regular rings
Commutative Algebra
2025-03-10 v2
Abstract
We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of R-modules agrees with its graded-injective (resp. graded-projective) dimension. The same is shown for the analogous dimensions based on FP-injective R-modules, and on flat R-modules.
Keywords
Cite
@article{arxiv.2409.08393,
title = {Homological dimensions of complexes over coherent regular rings},
author = {James Gillespie and Alina Iacob},
journal= {arXiv preprint arXiv:2409.08393},
year = {2025}
}
Comments
Minor corrections and updates