This M.Sc. thesis is based on the following paper. All rings are associative with unity and s ubrings have the same unity as the over ring , unless indica ted other wise; R denotes such a ring. The theory of Baer rings has its origins in Operator Theory in the sense that Kaplansky introduced Baer rings to isolate certain algebraic properties of von Neumann algebras. Recall a ring R is Baer if the right annihilator of each nonempty set (equivalently, left ideal) is generated by an idempotent. Clark generalized the Baer condition: a ring R is quasi-Baer if the right annihilator of each ideal is generated by an idempotent. Each of the conditions, Baer and quasi-Baer, has certain advantages over the other. In general, the Baer condition works well with one-sided ideals, whereas the quasi-Baer condition works well with ideals. For example, a regular (biregular) ring is Baer (quasi-Baer) if and only if the lattice of principal left ideals (principal ideals) is complete.