Modules with minimax Cousin cohomologies

Abstract

‎Let \(R\) be a commutative Noetherian ring with non-zero identity and let \(X\) be an arbitrary \(R\)-module. In this paper, we show that if all the cohomology modules of the Cousin complex for \(X\) are minimax, then the following hold for any prime ideal \(\mathfrak{p}\) of \(R\) and for every integer \(n\) less than \(X\), the height of \(\mathfrak{p}\):

(i) the \(n\)th Bass number of \(X\) with respect to \(\mathfrak{p}\) is finite;

(ii) the \(n\)th local cohomology module of \(X_\mathfrak{p}\) with respect to \(\mathfrak{p}R_\mathfrak{p}\) is Artinian.