Geodesic
Totally reflexive modules with respect to a semidualizing bimodule
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 385-402
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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.
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.
DOI : 10.1007/s10587-013-0024-2
Classification : 16D20, 16D40, 16E05, 16E10, 16E30
Keywords: semidualizing bimodule; totally reflexive module; Bass class; precover; preenvelope 
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     title = {Totally reflexive modules with respect to a semidualizing bimodule},
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     year = {2013},
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Zhang, Zhen; Zhu, Xiaosheng; Yan, Xiaoguang. Totally reflexive modules with respect to a semidualizing bimodule. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 2, pp. 385-402. doi: 10.1007/s10587-013-0024-2

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