A ring S is strongly π-regular if for every a ∈ S there exists n ≥ 1 such that an∈ an+1S. It is first shown that the dominion and the maximal epimorphic extension of any ring homomorphism α:R →,S, S strongly π-regular, are strongly π-regular. Several results of Schofield on perfect and semiprimary rings are special cases. As an application it is shown that a strongly π-regular ring is a Schur ring, generalizing Lenagan’s theorem for artinian rings. Further if S ⊆ R where S is commutative strongly π-regular then for any finitely generated MSM⊗SR = 0, implies M = 0 , although ⊗Sis not faithful on homomorphisms. Another application shows that the dominion of the natural map Z → S acts like a characteristic for a strongly π-regular ring S