Abstract
ABSTRACT We say a ring with identity is a generalized right (principally) quasi-Baer if for any (principal) right ideal I of R, the right annihilator of In is generated by an idempotent for some positive integer n, depending on I. The behavior of the generalized right (principally) quasi-Baer condition is investigated with respect to various constructions and extensions. The class of generalized right (principally) quasi-Baer rings includes the right (principally) quasi-Baer rings and is closed under direct product and also under some kinds of upper triangular matrix rings. The generalized right (principally) quasi-Baer condition is a Morita invariant property. Examples to illustrate and delimit the theory are provided.
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