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 $E(R/\underline m)$?
Keywords:
paper discuss flat covers injective modules noetherian ring commutative noetherian ring injective r module prove flat cover isomorphic prod att consequence answer xus question prime ideal does appear flat cover underline
Affiliations des auteurs :
Sh. Payrovi
1
;
M. Akhavizadegan
1
1
Imam Khomeini International University P.O. Box 288 Qazvin, Iran
@article{10_4064_cm96_1_9,
author = {Sh. Payrovi and M. Akhavizadegan},
title = {Structure of flat covers of injective modules},
journal = {Colloquium Mathematicum},
pages = {93--101},
year = {2003},
volume = {96},
number = {1},
doi = {10.4064/cm96-1-9},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm96-1-9/}
}
TY - JOUR
AU - Sh. Payrovi
AU - M. Akhavizadegan
TI - Structure of flat covers of injective modules
JO - Colloquium Mathematicum
PY - 2003
SP - 93
EP - 101
VL - 96
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm96-1-9/
DO - 10.4064/cm96-1-9
LA - en
ID - 10_4064_cm96_1_9
ER -
%0 Journal Article
%A Sh. Payrovi
%A M. Akhavizadegan
%T Structure of flat covers of injective modules
%J Colloquium Mathematicum
%D 2003
%P 93-101
%V 96
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm96-1-9/
%R 10.4064/cm96-1-9
%G en
%F 10_4064_cm96_1_9
Sh. Payrovi; M. Akhavizadegan. Structure of flat covers of injective modules. Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 93-101. doi: 10.4064/cm96-1-9
