RADIKAL SUPERNILPOTENT BERTINGKAT

Abstract

The development of Ring Theory motivates the existence of the development of the Radical Theory of Rings. This condition is motivated since there are rings which have properties other than those owned by the set ring of all integers. These rings are collected so that they fulfill certain properties and they are called radical classes of rings. As the development of science about how to separate the properties of radical classes of rings motivates the existence of supernilpotent radical classes. On the other hand, there exists the concept of graded rings. This concept can be generalized into the Radical Theory of Rings. Thus, the properties of the graded supernilpotent radical classes are very interesting to investigate. In this paper, some graded supernilpotent radical of rings are given and their construction will be described. It follows from this construction that the graded Jacobson radical is a graded supernilpotent radical.