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Let $\Gamma$ be a ring extension of $R$. We show the left $\Gamma$-module $U=\Gamma {\otimes }_{R}C$ with the endmorphism ring End${}_{\Gamma }U=\Delta$ is a generalized tilting module when ${}_{R}C$ is a generalized tilting module under some conditions.

Let $S$ and $R$ be two associative rings, let ${}_S{C}_R$ be a semidualizing $(S,R)$-bimodule. We introduce and investigate properties of the totally reflexive module with respect to ${}_S{C}_R$ and we give a characterization of the class of the totally $C_R$-reflexive modules over any ring $R$. Moreover, we show that the totally $C_R$-reflexive module with finite projective dimension is exactly the finitely generated projective right $R$-module. We then study the relations between the class of totally reflexive modules and the Bass class...