Classification of rings satisfying some Herstein's condition on the set of all non-nilpotents

摘要

Let R be a non-commutative ring with center C and let N be the set of all nilpotents of R. The following result is proved: If for every a is an element of RN, there exists an integer n(a) > 1, depending on a, such that a(n(a)) - a is an element of C, then R is one of five types whose structures can be determined abstractly. References: 10