Remarks on torsionfreeness and its applications
Commutative Algebra
2016-05-23 v2
Abstract
In this article, we shall characterize torsionfreeness of modules with respect to a semidualizing module in terms of the Serre's condition (S_n). As its applications, we give a characterization of Cohen-Macaulay rings R such that R_p is Gorenstein for all prime ideals p of height less than n, and we will give a partial answer of Tachikawa conjecture and Auslander-Reiten conjecture.
Cite
@article{arxiv.1408.3796,
title = {Remarks on torsionfreeness and its applications},
author = {Tokuji Araya and Kei-ichiro Iima},
journal= {arXiv preprint arXiv:1408.3796},
year = {2016}
}
Comments
9 pages, minor changes, title is revised