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- W2620894615 abstract "Let $S$ and $R$ be rings and $_SC_R$ a (faithfully) semidualizing bimodule. We introduce and study $C$-weak flat and $C$-weak injective modules as a generalization of $C$-flat and $C$-injective modules (J. Math. Kyoto Univ. 47(2007), 781-808) respectively, and use them to provide additional information concerning the important Foxby equivalence between the subclasses of the Auslander class $mathcal{A}_C(R)$ and that of the Bass class $mathcal{B}_C(S)$. Then we study the stability of Auslander and Bass classes, which enables us to give some alternative characterizations of the modules in $mathcal{A}_C(R)$ and $mathcal{B}_C(S)$. Finally we consider an open question which is closely relative to the main results (Proc. Edinb. Math. Soc. 48(2005), 75-90), and discuss the relationship between the Bass class $mathcal{B}_C(S)$ and the class of Gorenstein injective modules." @default.
- W2620894615 created "2017-06-09" @default.
- W2620894615 creator A5063634391 @default.
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- W2620894615 date "2017-06-02" @default.
- W2620894615 modified "2023-09-25" @default.
- W2620894615 title "Foxby equivalence relative to $C$-weak injective and $C$-weak flat modules" @default.
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- W2620894615 doi "https://doi.org/10.48550/arxiv.1706.00568" @default.
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