Commutativity in Prime Gamma Rings with Jordan Left Derivations

Abstract

Let M be a 2–torsion free prime ?–ring and let d: M?M  be a Jordan left derivation . In this article, we show that under a suitable condition every nonzero Jordan left derivation on M  induces the commutativity of M and accordingly d is a left derivation of M.

Key words: Jordan left derivation, prime ?– ring, left derivation, ?– ring.