On Artinian Modules Over Duo Rings

Abstract

The well-known method, which reduces the study of Artinian modules over commutative rings to the study of Artinian modules over quasi-local rings, is extended to the study of these modules over duo rings. The duals of Krull Intersection Theorem and Nakayama's Lemma are proved for Artinian modules over a large class of duo rings. We also give an upper bound for the length of a duo ring R in terms of the length of a faithful R-module. This generalizes a well-known result of Schur concerning the cardinality of a maximal linearly independent set of commuting matrices.