{"title":"Homological dimensions of complexes over coherent regular rings","authors":"James Gillespie, Alina Iacob","doi":"arxiv-2409.08393","DOIUrl":null,"url":null,"abstract":"We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends\nfrom Noetherian to coherent rings. In particular, a coherent ring R is regular\nif and only if the injective (resp. projective) dimension of each complex X of\nR-modules agrees with its graded-injective (resp. graded-projective) dimension.\nThe same is shown for the analogous dimensions based on FP-injective R-modules,\nand on flat R-modules.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08393","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.