In [15], Kaplansky introduced Baer rings as rings in which every right (left) annihilator ideal is generated by an idempotent. According to Clark [9], a ring R is called quasi-Baer if the right annihilator of every right ideal is generated (as a right ideal) by an idempotent. Further works on quasi-Baer rings appear in [4, 6, 17]. Recently, Birkenmeier et al. [8] called a ring R to be a right (...

An ideal I of a ring R is called right Baer-ideal if there exists an idempotent e 2 R such that r(I) = eR. We know that R is quasi-Baer if every ideal of R is a right Baer-ideal, R is n-generalized right quasi-Baer if for each I E R the ideal In is right Baer-ideal, and R is right principaly quasi-Baer if every principal right ideal of R is a right Baer-ideal. Therefore the concept of Baer idea...

A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any element a ∈ R. We consider left APP-property of the skew formal power series ring R[[x;α]] where α is a ring automorphism of R. It is shown that if R is a ring satisfying descending chain condition on right annihilators then R[[x;α]] is left APP if and only if for any sequence (b0, b1, ....

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

the notions of quasi-prime submodules and developed  zariski topology was introduced by the present authors in cite{ah10}. in this paper we use these notions to define a scheme. for an $r$-module $m$, let $x:={qin qspec(m) mid (q:_r m)inspec(r)}$. it is proved that $(x, mathcal{o}_x)$ is a locally ringed space. we study the morphism of locally ringed spaces induced by $r$-homomorphism $mrightar...

Abstract Let R be a ring and let M an -module with $$S={\text {End}}_R(M)$$ S = End R ( M ) . The module is called quasi-dual Baer if for every fully invari...