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Structure of flat covers of injective modules

Sh. Payrovi; M. Akhavizadegan — 2003

Colloquium Mathematicae

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 $\prod_{p \in A t t_{R} (E)} T_{p}$ . 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/m̲)?

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