Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 87-95, 2017

Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi

Received July 13, 2015.   First published February 24, 2017.

Elham Tavasoli, Maryam Salimi, Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran, e-mail: elhamtavasoli@ipm.ir, maryamsalimi@ipm.ir

Abstract: Let $R$ be a commutative Noetherian ring and let $C$ be a semidualizing $R$-module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to $C$ which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every $G_C$-injective module $G$, the character module $G^+$ is $G_C$-flat, then the class $\mathcal{GI}_C(R)\cap\mathcal{A}_C(R)$ is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class $\mathcal{GI}_C(R)\cap\mathcal{A}_C(R)$ is covering.

Keywords: semidualizing module; $G_C$-flat module; $G _C$-injective module; cover; envelope

Classification (MSC 2010): 13D05, 13D45, 18G20

DOI: 10.21136/CMJ.2017.0379-15

Full text available as PDF.


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