A Note on Derivations II

Abstract

In a previous note on derivations [1] we determined the structure of a prime ring R which has a derivation d≠0 such that the values of d commute, that is, for which d ( x ) d ( y ) = d ( y ) d ( x ) for all x, y∈R . Perhaps even more natural might be the question: what elements in a prime ring commute with all the values of a non-zero derivation? We address ourselves to this question here, and settle it.