Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 3
Gorenstein transpose with respect to a semidualizing bimodule
- Sayfa
- 404–417
- DOI
- —
Özet
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.
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.