Remarks on torsionfreeness and its applications

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.

9 pages, minor changes, title is revised

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