Gorenstein Homological Dimensions and Auslander Categories with Respect to a Semidualizing Module
Received:March 19, 2012  Revised:November 22, 2012
Key Word: semidualizing modules   $C$-Gorenstein injective modules   $C$-Gorenstein projective modules   $C$-Gorenstein flat modules   Auslander categories.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11261050).
 Author Name Affiliation Chunxia ZHANG Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China Limin WANG Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China Zhongkui LIU Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China
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Let $R$ be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing $R$-module $C$, and we give some connections between $C$-Gorenstein homological dimensions and the Auslander categories of $\hat{R}$.