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