STRUCTURE OF THE FLAT COVERS OF ARTINIAN MODULES Payrovi, S.H.;
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 , where is the completion of a free -module. Also, we construct a minimal flat resolution for R/xR-module 0: from a given minimal flat resolution of A, when n is a non-unit and non-zero divisor of R such that A = . This result leads to a description of the structure of a minimal flat resolution for , nth local cohomology module of R with respect to the ideal , over a local Cohen-Macaulay ring (R, ) of dimension n.