Generalizations of von Neumann regular rings, PP rings, and Baer rings

摘要

We introduce the notions of IDS modules, IP modules, and Baer* modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer* modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer* modules.