Abstract
ABSTRACTIn this article, we shall characterize torsionfreeness of modules with respect to a semidualizing module in terms of the Serre’s condition (Sn). As its applications, we give a characterization of Cohen-Macaulay rings R such that R𝔭 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.
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