Structure of flat covers of injective modules
Volume 96 / 2003
Colloquium Mathematicum 96 (2003), 93-101
MSC: 13C11, 13E05.
DOI: 10.4064/cm96-1-9
Abstract
The aim of this paper is to discuss the flat covers of injective modules over a Noetherian ring. Let $R$ be a commutative Noetherian ring and let $E$ be an injective $R$-module. We prove that the flat cover of $E$ is isomorphic to $\prod _{p\in {\rm Att}_{R}(E)}T_p$. As a consequence, we give an answer to Xu's question [10, 4.4.9]: for a prime ideal $p$, when does $T_p$ appear in the flat cover of $E(R/\underline m)$?
