  We introduce graded gamma rings from a more general point of view via methods
developed by Krasner and Halberstadt for graded rings. We propose three
equivalent aspects of studying graded gamma rings, nonhomogeneous,
semihomogeneous and homogeneous. The graded Jacobson radical of a graded gamma
ring is introduced and its elementwise description is given. Also, a relation
between the graded Jacobson radical and the Jacobson radical of a graded gamma
ring is examined.
