Abstract

Let $R$ be a commutative Noetherian ring. The aim of this paper is studying the properties of relative Gorenstein modules with respect to a dualizing module. It is shown that every quotient of an injective module is $G_{C}$-injective, where $C$ is a dualizing $R$-module with $id_{R}(C) \leq 1$. We also prove that if $C$ is a dualizing module for a local integral domain, then every $G_{C}$-injective $R$-module is divisible. In addition, we give a characterization of dualizing modules via relative Gorenstein homological dimensions with respect to a semidualizing module.

Keywords: semidualizing; dualizing; $C$-injective; $G_{C}$-injective.

MSC: 13D05, 13D45, 18G20

Pages:  118$-$125     

Volume  69 ,  Issue  2 ,  2017