New Characterizations of Dualizing Modules |
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Authors: | Xi Tang |
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Institution: | 1. Department of Mathematics , Nanjing University , Nanjing , China tx5259@sina.com.cn |
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Abstract: | Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a semidualizing module to be dualizing in terms of special homological properties of module categories. The purpose of this article is twofold: first, it aims at improving Christensen's and Takahashi et al.'s characterizations of dualizing modules; secondly, while applying these criteria to the ring itself, we not only recover some results of Jenda and Xu, respectively, but also obtain a new characterization of Gorenstein rings. |
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Keywords: | Auslander class Bass class C-flat dimension C-injective dimension Dualizing module Gorenstein homological dimension Semidualizing module |
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