On relative Gorenstein homological dimensions with respect to a dualizing module

Maryam Salimi

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 $i{d}_R\left(C\right)\le 1$. 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.

Classification (MSC2000): 13D05; 13D45, 18G20

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