A+ CATEGORY SCIENTIFIC UNIT

Structure of flat covers of injective modules

Volume 96 / 2003

Sh. Payrovi, M. Akhavizadegan 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 $E(R/\underline m)$?

Authors

  • Sh. PayroviImam Khomeini International University
    P.O. Box 288
    Qazvin, Iran
    e-mail
  • M. AkhavizadeganImam Khomeini International University
    P.O. Box 288
    Qazvin, Iran
    e-mail

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