Strongly irreducible ideals of a commutative ring

An ideal I of a ring R is said to be strongly irreducible if for ideals J and K of R, the inclusion J∩K I implies that either J I or K I. The relationship among the families of irreducible ideals, strongly irreducible ideals, and prime ideals of a commutative ring R is considered, and a characterization is given of the Noetherian rings which contain a non-prime strongly irreducible ideal.