MATEMATIČKI VESNIK Vol. 69, No. 2, pp. 118–125 (2017) 

On relative Gorenstein homological dimensions with respect to a dualizing moduleMaryam SalimiDepartment of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran Email: maryamsalimi@ipm.irAbstract: 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 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 24 Feb 2017. This page was last modified: 17 Mar 2017.
© 2017 Mathematical Society of Serbia (Društvo matematičara Srbije)
