GENERALIZED JORDAN LEFT DERIVATION ON SOME GAMMA RING

Abstract

In this paper we define a Generalized Jordan left derivation on  -ring and show thatthe existence of a non-zero generalized Jordan left derivation D on a completely prime  -ring implies D is a generalized left derivation .Furthermore we show that every generalizedJordan left derivation on  -ring has a commutator left non-zero divisor is a generalizedleft derivation on  -ring.Key wards :  -ring, prime  -ring, prime  -ring , left derivation, ,Jordan left derivation,generalized Jordan left derivation .