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.