Abstract. Although the characterization of ring derivations has an extensive literature, up to now, all of the characterizations have had the following form: additivity and another property imply that the function in question is a derivation. The aim of this note is to point out that derivations can be described via a single equation.

AMS Subject Classification (1991): 39B50, 13N15

Keyword(s): derivation, Cauchy difference, cocycle equation

Received July 22, 2010, and in revised form March 7, 2011. (Registered under 46/2010.)