On the Strong (A)-Rings of Mahdou and Hassani

A (commutative unital) ring R with only finitely many minimal prime ideals (for instance, a Noetherian ring) is reduced and a strong (A)-ring if and only if R is an integral domain. Thus, the smallest reduced ring which has Property A but is not a strong (A)-ring is ${\mathbb{Z}_{2} \times \mathbb{Z}_{2}}$ . A Noetherian ring R is a strong (A)-ring if and only if Ass _R (R) has a unique maximal element.