Brown-McCoy Radical in Restricted Graded Version

Abstract

Some conjectures related to the radical theory of rings are still open. Hence, the research on the radical theory of rings is still being investigated by some prominent authors. On the other hand, some results on the radical theory of rings can be implemented in another branch or structure. In radical theory, it is interesting to bring some radical classes into graded versions. In this chance, we implement a qualitative method to conduct the research to bring the Brown-McCoy radical class to the restricted graded Brown-McCoy radical class as research objective. We start from some known facts on the Brown-McCoy radical class and furthermore, let G be a group, we explain the Brown-McCoy radical restricted with respect to the group G. The result of this paper, we describe the Brown-McCoy radical in restricted graded version and it is denoted by G^G. Furthermore, we also give the fact by explaining G^G (A)=(〖G(A))〗_G, for any ring A, as the final outcome of this paper.