Relative Gorenstein injective covers with respect to a semidualizing module

Czechoslovak Mathematical Journal

Elham Tavasoli, Maryam Salimi¹ 

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

DOI  :  10.21136/CMJ.2017.0379-15

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  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.

【 授权许可】

Unknown