English

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.

Keywords

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

R2 v1 2026-06-22T05:31:09.531Z