$\pi$-BAER $\ast$-RINGS

Abstract

A * -ring R is called a π-Baer * -ring, if for any projection invariant left ideal Y of R, the right annihilator of Y is generated, as a right ideal, by a projection. In this note, we study some properties of such * -rings. We indicate interrelationships between the π-Baer * -rings and related classes of rings such as π-Baer rings, Baer * -rings, and quasi-Baer * -rings. We announce several results on π-Baer * -rings. We show that this notion is well-behaved with respect to polynomial extensions and full matrix rings. Examples are provided to explain and delimit our results.