Characterizing local rings via homological dimensions and regular sequences
交换代数
2007-05-23 v2
摘要
Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If G_C-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length at most d-t then either G_C-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.
引用
@article{arxiv.math/0401031,
title = {Characterizing local rings via homological dimensions and regular sequences},
author = {Shokrollah Salarian and Sean Sather-Wagstaff and Siamak Yassemi},
journal= {arXiv preprint arXiv:math/0401031},
year = {2007}
}
备注
Final version, to appear in J. Pure Appl. Algebra. 9 pages. Uses XY-pic