English

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.