We define a ring R to be right c P-Baer if the right annihilator of a cyclic projective right R-
module in R is generated by an idempotent. This class of rings generalizes the class of right …

A ring R is called “quasi-Baer” if the right annihilator of every right ideal is generated, as a
right ideal, by an idempotent. It can be seen that a quasi-Baer ring cannot be a right …

We say a ring R is π-Baer if the right annihilator of every projection invariant left ideal of R is
generated by an idempotent element of R. In this paper, we study connections between the …

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 …

A ring R is a left AIP-ring if the left annihilator of any ideal of R is pure as a left ideal.
Equivalently, R is a left AIP-ring if R modulo the left annihilator of any ideal is flat. This class …

Throughout this paper R denotes an associative ring with unity. Recall from [Ka2) that R is a
Baer ring if the right annihilator of every nonempty subset of R is generated, as a right ideal …

A module MR is called right principally quasi-Baer (or simply right pq-Baer) if the right
annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let …

We say a ring with unity is right principally quasi-Baer (or simply, right pq-Baer) if the right
annihilator of a principal right ideal is generated (as a right ideal) by an idempotent. This …

We say a ring R with unity is weakly principally quasi-Baer or simply (weakly pq-Baer) if the
right annihilator of a principal right ideal is right s-unital by right semicentral idempotents …

We say that a*-ring R is a generalized quasi-Baer*-ring if for any ideal I of R, the right
annihilator of I n is generated, as a right ideal, by a projection, for some positive integer n …