NORMALITY CONDITIONS AND COMMUTATIVITY THEOREMS FOR RINGS

Abstract

Let R be a ring with center C, and let N the set of nilpotent elements. nn

Supposethatforeachx,y∈R\N,xy−xy ∈N∩C,wheren>1 is a fixed integer. We shall present conditions for R to be commutative, non-commutative, normal and periodic.