- Turkish Journal of Mathematics
- Vol: 37 Issue: 3
- Gorenstein transpose with respect to a semidualizing bimodule
Gorenstein transpose with respect to a semidualizing bimodule
Authors : Zengfeng Liu, Xiaoguang Yan
Pages : 404-417
Doi:10.3906/mat-1109-50
View : 13 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
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