Semiprime rings with bounded indices of nilpotent elements

Abstract

This paper deals with the structure of semiprime rings for which the indices of the nilpotent elements are bounded. It is shown that the complete right ring of quotients of such a ring is a regular, right self-injective ring in which each finitely generated ideal is generated by a central idempotent. The indices of the nilpotent elements of the factor ring of such a ring with respect to a minimal prime ideal do not exceed the upper bound of the indices of the nilpotent elements of the original ring. A criterion for the regularity (in the sense of von Neumann) of such rings is obtained. Also investigated are right completely idempotent rings with bounded indices of nilpotent elements (it is shown, in particular, that each nonzero ideal of such a ring contains a nonzero central idempotent).