The author gives certain details of his well-known example of the ring which was used by Handelman and Lawrence to show that the left and right strongly prime radicals of a ring need not coincide. The example is used to prove that the classes of right strongly prime rings, left strongly prime rings and uniformly strongly prime rings are not normal classes and that the corresponding radicals are not normal radicals. It is also proved that, in the category of rings with identity, strongly prime and uniformly strongly prime are Morita invariants, as is the semisimplicity with respect to strongly primeness.