Abstract: The concept of the virtually Baer modules is introduced, giving an example to illustrate that virtually Baer modules are a proper generalization of Baer modules. Under certain conditions, the closure of virtually Baer modules to direct summands is given. The relationships between virtually Baer modules and GSIP-modules as well as generalized SSIP-modules are discussed. Subsequently, new descriptions of semisimple artinian rings and right V-rings are derived from these discussions.

Key words: virtually Baer module, Baer module, GSIP module, semisimple artinian ring, V-ring