Abstract
In this paper, we introduce the concept of rings with right (left) weak property (A) which is a generalization of rings with right (left) property (A). A ring [Formula: see text] has right (left) weak property (A) if every finitely generated two-sided ideal [Formula: see text] of [Formula: see text] with [Formula: see text], there exists nonzero [Formula: see text] [Formula: see text] such that [Formula: see text] [Formula: see text]. Further, we study various extensions of rings with weak property (A) including matrix rings, polynomial rings and Ore extensions.
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