Gorenstein transpose with respect to a semidualizing bimodule

Authors : Zengfeng LIU, Xiaoguang YAN

Pages : 404-417

Doi:10.3906/mat-1109-50

View : 12 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let S and R be rings and SCR 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 GC-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 Rop 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 GC-projective. Finally we investigate some homological properties of the C-Gorenstein transpose of a given module.
Keywords : Semidualizing bimodule, GC projective, C transpose, n C torsionfree, C Gorenstein transpose