Baer semisimple modules and Baer rings

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.