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Keywords:
semidualizing bimodule; totally reflexive module; Bass class; precover; preenvelope
semidualizing bimodule; totally reflexive module; Bass class; precover; preenvelope
Summary:
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 with respect to a semidualizing bimodule. The paper contains several results which are new in the commutative Noetherian setting.
References:
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