Abstract
Let $R$ and $S$ be rings and ${}_SC_R$ a faithfully semidualizing bimodule. A left $S$-module $M$ is called \textit{Ding $C$-projective} if there exists an exact sequence of $C$-projective left $S$-modules \[ X=\cdots \rightarrow C\otimes_{R} P_{1}\rightarrow C\otimes_{R} P_{0}\rightarrow C\otimes_{R} P^{0}\rightarrow C\otimes_{R} P^{1}\rightarrow \cdots \] such that $M\cong\mbox{Coker\,}(C\otimes_{R} P_{1}\rightarrow C\otimes_{R} P_{0})$ and the complexes $\mbox{Hom}_S(C\otimes_{R}P, X)$ and $\mbox{Hom}_S(X,C\otimes_{R}F)$ are exact for any projective left $R$-module $P$ and any flat left $R$-module $F$. The properties of Ding $C$-projective modules and dimensions are given. Among others, the Foxby equivalences between some subclasses of the Auslander class and the Bass class are also investigated.
Citation
Chunxia Zhang. Limin Wang. Zhongkui Liu. "Ding projective modules with respect to a semidualizing bimodule." Rocky Mountain J. Math. 45 (4) 1389 - 1411, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1389
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