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

Abstract

We introduce the notions of IDS modules, IP modules, and Baer^* modules, which are new generalizations of von Neumann regular rings, PPrings, 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.

Keywords

IDS Module / IP module / Baer∗ module / von Neumann regular ring / PP ring / Baer ring

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