Remarks on torsionfreeness and its applications |
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| Authors: | Tokuji Araya |
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| Affiliation: | Department of Applied Science, Faculty of Science, Okayama University of Science, Kitaku, Okayama, Japan |
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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 (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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| Keywords: | Gorenstein semidualizing module Serre’s condition syzygy Tachikawa conjecture torsionfree |
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