Baer Endomorphism Rings and Closure Operators

Abstract

A Baer ring is a ring in which every right (and left) annihilator ideal is generated by an idempotent. Generalizing quite naturally from the fact that the endomorphism ring of a vector space is a Baer ring, Wolfson [5; 6] investigated questions such as when the endomorphism ring of a free module is a Baer ring, and when the ring of continuous linear transformations on a pair of dual vector spaces is a Baer ring. A further generalization was made in [7], where the question of when the endomorphism ring of a torsion-free module over a semiprime left Goldie ring is a Baer ring was treated.