S.K. Berberian
Baer rings and Baer *-rings
(902K, pdf)

ABSTRACT.  An exposition of Irving Kaplansky's theory of Baer rings (annihilator ideals are idempotent-generated) and Baer 
 *-rings (annihilator ideals are projection-generated), with examples from von Neumann algebras, AW*-algebras, 
 self-injective regular rings, complete *-regular rings, continuous geometries