STRUCTURE OF THE FLAT COVERS OF ARTINIAN MODULES

Title & Authors
STRUCTURE OF THE FLAT COVERS OF ARTINIAN MODULES
Payrovi, S.H.;

Abstract
The aim of the Paper is to Obtain information about the flat covers and minimal flat resolutions of Artinian modules over a Noetherian ring. Let R be a commutative Noetherian ring and let A be an Artinian R-module. We prove that the flat cover of a is of the form $\small{\prod_{p\epsilonAtt_R(A)}T-p}$, where $\small{Tp}$ is the completion of a free $\small{R_{p}}$-module. Also, we construct a minimal flat resolution for R/xR-module 0: $\small{_AX}$ from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = $\small{\chiA}$. This result leads to a description of the structure of a minimal flat resolution for $\small{{H^n}_{\underline{m}}(R)}$, nth local cohomology module of R with respect to the ideal $\small{\underline{m}}$, over a local Cohen-Macaulay ring (R, $\small{\underline{m}}$) of dimension n.
Keywords
Artinian module;flat cover;minimal flat resolution;
Language
English
Cited by
1.
Minimal Flat Resolutions of Artinian Modules, Algebra Colloquium, 2005, 12, 03, 443
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