Vol. 69, No. 2, pp. 118–125 (2017)

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On relative Gorenstein homological dimensions with respect to a dualizing module

Maryam Salimi

Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran E-mail: maryamsalimi@ipm.ir

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)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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Electronic fulltext finalized on: 24 Feb 2017. This page was last modified: 17 Mar 2017.

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