On generalized AIP-rings

Abstract

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.