SYSTEM OF PARAMETERS FOR PSEUDO COHEN-MACAULAY MODULES

Abstract

Throughout, (A,m)denotes acommutativeNoetherian localring withthe maximalideal m and M a finitely generated A-modulewith dim M = d. We denote by QM(x) the submodule of M defined by QM(x)= n>0 (xn+1 1 ,...,xn+1 d )M : xn 1 ···xn d, where x =(x1,...,xd) is a system of parameters on M. The submodule QM(x) is a useful tool in the study of Monomial Conjecture, determinant maps, top local cohomology modules, modules of generalized fractions... (see [25], [4], [6] and [8]).