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Currently displaying 1 – 2 of 2

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Generalized tilting modules over ring extension

Zhen Zhang — 2019

Czechoslovak Mathematical Journal

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

Totally reflexive modules with respect to a semidualizing bimodule

Zhen Zhang; Xiaosheng Zhu; Xiaoguang Yan — 2013

Czechoslovak Mathematical Journal

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...

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