On Strong (A)-Rings

In this paper, we introduce a strong property (A) as follows: A ring R is called satisfying strong property (A) if every finitely generated ideal of R which is generated by a finite number of zero-divisors elements of R, has a non zero annihilator. We study the transfer of property (A) and strong property (A) in trivial ring extensions and amalgamated duplication of a ring along an ideal. We also exhibit a class of rings which satisfy property (A) and do not satisfy strong property (A).