# On graded Brown--McCoy radicals of graded rings

## TL;DR

This paper explores the properties and characterizations of graded Brown--McCoy radicals in graded rings, establishing relationships between different types of these radicals and the classical radical.

## Contribution

It provides new characterizations of the graded Brown--McCoy radical and links the large graded Brown--McCoy radical to the classical radical in graded rings.

## Key findings

- Multiple characterizations of the graded Brown--McCoy radical.
- The large graded Brown--McCoy radical is the largest homogeneous ideal within the classical radical.
- Established the relationship between graded and classical Brown--McCoy radicals.

## 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.