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.