Gorenstein transpose with respect to a semidualizing bimodule

Authors: ZENGFENG LIU, XIAOGUANG YAN

Abstract: Let S and R be rings and _SC_R be a semidualizing bimodule. We first give the definitions of C-transpose and n-C-torsionfree and give a criterion for a module A to be G_C-projective by some property of the C-transpose of A. Then we introduce the notion of C-Gorenstein transpose of a module over two-sided Noetherian rings. We prove that a module M in \mod R^{op} is a C-Gorenstein transpose of a module A \in \mod S if and only if M can be embedded into a C-transpose of A with the cokernel G_C-projective. Finally we investigate some homological properties of the C-Gorenstein transpose of a given module.

Keywords: Semidualizing bimodule, G_C-projective, C-transpose, n-C-torsionfree, C-Gorenstein transpose

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