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arXiv · 1904.00033

On graded Brown--McCoy radicals of graded rings

Emil Ilić-Georgijević
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Abstract

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.

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Emil Ilić-Georgijević. 2019-03-29. On graded Brown--McCoy radicals of graded rings. https://doi.org/10.1142/s0219498816501437

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