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arXiv · 1408.3796

Remarks on torsionfreeness and its applications

Tokuji Araya·Kei-ichiro Iima
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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.

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Tokuji Araya, Kei-ichiro Iima. 2014-08-17. Remarks on torsionfreeness and its applications. https://arxiv.org/abs/1408.3796

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