On rings with annihilator condition

Huckaba and Keller say a commutative ring R has Property (A) if every finitely generated ideal of R consisting entirely of zero divisors has nonzero annihilator. Hong et al. extend Property (A) to noncommutative rings and show that neither right self-injective rings nor von Neumann regular rings have Property (A), in general. We continue in this paper the study of rings with Property (A), and consider conditions under which right FP-injective rings, mininjective rings, strongly right AB rings and rings with quasi-IFP have Property (A)