On graded Brown-McCoy radicals of graded rings

摘要

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.