CHARACTERIZATION THEOREMS OF S-ARTINIAN MODULES

Abstract

A module X over a commutative ring A is called S-Artinian, where S is a given multiplicatively closed subset of A, if every descending chain of sub-modules of X is S-stationary. Using this concept, we give many examples, properties and S-versions of several different known results. Also, we characterize S-Artinian in terms of several modules and rings. For instance, X is S-Artinian if and only if every factor module X/Y is a finitely S-cogenerated A-module.