On generalized AIP-rings

Document Type: Regular Paper


Department of Mathematics and Computer Science, Shahed University, Tehran, Iran


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.