Graded gamma rings

Abstract: 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.