CHAIN CONDITIONS ON QUOTIENT FINITE DIMENSIONAL MODULES

Abstract

This paper is motivated by a recent work of C. Faith [9] who has proved that a quotient finite dimensional module which satisfies the ascending chain condition on subdirectly irreducible submodules is Noetherian. A natural question to ask (also raised by Faith [11]) is whether its dual holds true. We answer this in the affirmative, and provide a characterization of Artinian modules dual to Faith's Theorem. We also extend these results to the more general settings of dual Krull dimension and Krull dimension respectively.