Ascent and descent of Artinian module structures under flat base changes

Abstract

Let $\ddot{I}†:R\to S$ be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between $R$ and $S$ are investigated. For an Artinian $R$-module $A$, the structure of $A{\otimes }_{R}S$ is described. As an application, the Artinianess of certain local cohomology modules is clarified.

10 pages