Examples of strongly π-regular rings

Our study in this note is concentrated on extending the class of strongly π-regular rings, observing the structures of them. We call a ring locally finite if every finite subset in it generates a finite semigroup multiplicatively. We first study the structures of locally finite rings and then study relations between locally finite rings and other related rings. We also study the strong π-regularity of some kinds of semiperfect rings with nil Jacobson radicals.