NORMALITY CONDITIONS AND COMMUTATIVITY THEOREMS FOR RINGS

Abstract

Let R be a ring with centerC, and letN the set of nilpotent elements. Suppose that for each x, y ∈ R\N,xny −xyn ∈ N ∩ C, wheren>1 is a fixed integer. We shall present conditions for R to be commutative, non-commutative, normal and periodic.