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.
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