The Conditions Of Morita Context Ring To Be (Pincipally) Quasi-Baer Rings

The ring theories, which mainly study the properties of algebraic structure with two algebraic operations and the correlation of different algebraic structure, play an important role in Algebra, among which Baer-ring is one of the most active research branch. Birkenmeier G. F showed that biregular ring and quasi-Baer ring are p. q.-Baer and also proved that right p. q.-Baer is Morita invariant and is closed under direct products. But Birkenmeier G. F did not proved that Baer and quasi-Baer are Morita invariants.This paper studies that whether Baer is Morita invariant. From the counterexam-ple of 2 x 2 matrix ring over the ring of integer modulo 2, we know that Baer is not Morita invariant; then we study the conditions for which Morita Context rings with two zero homomorphisms can be Baer, quasi-Baer and right p. q.-Baer. We show that Morita Context ring with two zero modules would be Baer ring and quasi-Baer ring, then we extended the study to 3 x 3 Morita Context ring. By Morita Context theory, we extended the class of Baer ring, quasi-Baer ring and right p.q.-Baer ring.