%0 Journal Article %T On generalized AIP-rings %J Iranian Journal of Science %I Springer %Z 2731-8095 %A Anzani, M. %A Haj Seyyed Javadi, H. %D 2014 %\ 10/06/2014 %V 38 %N 3.1 %P 337-342 %! On generalized AIP-rings %K Baer rings %K quasi-Baer rings %K p.p.-rings %K annihilators %K idempotent %K s-unital ideal %R 10.22099/ijsts.2014.2431 %X 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 several examples to show the applicability and limitation of this class of rings. %U https://ijsts.shirazu.ac.ir/article_2431_b70a4ae8b1f1ef300c2a18358868247a.pdf