Principally π-Baer rings

We say a ring is right principally \pi-Baer (or simply right p.\pi-Baer) if an idempotent generates the right annihilator of every projection invariant principal left ideal. The class of right p.\pi-Baer rings includes the von Neumann regular rings (and hence right p.p-rings) and all \pi-Baer rings. This class of rings is closed under direct products. The behavior of the right p.\pi-Baer condition is investigated concerning various constructions and extensions. Moreover, we extend a theorem of Kist for commutative p.p-rings to right p.\pi-Baer rings for which every prime ideal contains a unique minimal prime ideal without using topological arguments.

کلیدواژه ها:

p.p ring ، Baer ring ، quasi-Baer ring ، principally quasi-Baer ring ، π-Baer ring ، p.π-Baer ring ، semicentral idempotent