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This paper is a continuation of our previous article [9]. We introduce an “artinian dimension” of modules, which allows us to study isoartinian modules, and an “isoradical” of a module, which is the analogue of the (Jacobson) radical of a module. We study the modules generated by isosimple submodules, and modules of finite I-length, which are analogous to modules of finite composition length.
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≥M1≥M2≥… of submodules of M, there exists an index n≥1 such that Mn is isomorphic to Mi for every i≥n. A ring R is right isoartinian if RR is an isoartinian module. Similarly we define isonoetherian and isosimple modules and rings. We determine...
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