1. New Characterizations of Dualizing Modules.
- Author
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Tang, Xi
- Subjects
- *
MODULES (Algebra) , *COMMUTATIVE algebra , *NOETHERIAN rings , *RING theory , *GORENSTEIN rings , *ALGEBRAIC geometry , *ALGEBRAIC fields - 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. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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