Modules with chain conditions up to isomorphism

We study modules with chain conditions up to isomorphism, in the following sense. We say that a right module M is isoartinian if, for every descending chain M >= M-1 >= M-2 >= center dot center dot center dot of submodules of M, there exists an index n >= 1 such that M-n is isomorphic to M-i for every i >= n. A ring R is right isoartinian if R-R is an isoartinian module. Similarly we define isonoetherian and isosimple modules and rings. We determine a number of properties of such modules and rings, giving several examples. For instance, we prove that a ring R is a right isoartinian semiprime right noetherian ring if and only if R is a finite direct product of matrix rings over principal right ideal domains. (C) 2016 Elsevier Inc. All rights reserved.