Artinian modules over commutative rings

Abstract

In 5, I provided a method whereby the study of an Artinian module A over a commutative ring R (throughout the paper, R will denote a commutative ring with identity) can, for some purposes at least, be reduced to the study of an Artinian module A' over a complete (Noetherian) local ring; in the latter situation, Matlis' duality 1 (alternatively, see 6, ch. 5) is available, and this means that the investigation can often be converted into a dual one about a finitely generated module over a complete (Noetherian) local ring.