Quasi-Baer and Quasi-Extending Rings
by
Gary F. Birkenmeier
University of Southwestern Louisiana

Let R denote an associative ring with unity. R is called QUASI-BAER if the right annihilator of every ideal of R is generated, as a right ideal, by an idempotent. R is called RIGHT QUASI-EXTENDING if every ideal of R is right essential in a right ideal of R generated by an idempotent. The classes of quasi-Baer rings and right quasi-extending rings effectively generalize the classes of Baer rings and right CS rings, respectively. One advantage of studying these generalized classes is that they are closed with respect to certain extensions (e.g., formation of full and upper triangular n-by-n matrix rings) for which the classes of Baer rings and right CS rings are not! The connections and distinctions between the classes of quasi-Baer rings and right quasi-extending rings will be discussed, and applications to the classes of Baer rings and right CS rings will be made. Examples to illustrate and delimit the theory will be provided.

Date received: December 3, 1998