: A commutative ring R has Property (A) if every finitely generated ideal of R consisting entirely of zerodivisors has a nonzero annihilator. It is continued in this thesis the study of rings with Property (A). It is extended Property (A) to noncommutative rings, and study such rings. Moreover, it is studied several extensions of rings with Property (A) including matrix rings, polynomial rings, power series rings and ideals of rings with Property (A) is compact.
