On graded Brown--McCoy radicals of graded rings

We investigate the graded Brown–McCoy and the classical Brown–McCoy radical of a graded ring, which is the direct sum of a family of its additive subgroups indexed by a nonempty set, under the assumption that the product of homogeneous elements is again homogeneous. There are two kinds of the graded Brown–McCoy radical, the graded Brown–McCoy and the large graded Brown–McCoy radical of a graded ring. Several characterizations of the graded Brown–McCoy radical are given, and it is proved that the large graded Brown–McCoy radical of a graded ring is the largest homogeneous ideal contained in the classical Brown–McCoy radical of that ring.