Baer semisimple modules and Baer rings

Abstract

We consider Baer rings and Baer semisimple R-modules which are generalizations of semisimple modules. Several characterization theorems of Baer semisimple modules are obtained. In particular, we prove that a ring R is a Baer ring if and only if R itself, regarded as a regular R-module, is Baer semisimple.