Artinian dimension and isoradical of modules

Abstract

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.