| For convenience, a ring whose units satisfies a group identity will be called a GI-ring. We show that GI-rings have the following properties which are also properites of PI-rings. (1) Any GI-ring is Dedekind finite (von Neumann finite). (2) Nilpotent elements of a semiprime GI-ring have bounded index. (3) The Kurosh problem has a positive answer for GI-algebras, namely, any algebraic GI-algebra is locally finite. |