A note on the graded isoradical of a graded ring

摘要

We study the graded isoradical of a ring graded by a group. In particular, we compare the graded isoradical and the classical isoradical of a graded ring, examine the question of how the (graded) isoradical of a graded ring depends on the classical isoradical of a ring which corresponds to the identity element of the grading group, and we also give some sufficient conditions under which the classical isoradical of a graded ring is homogeneous. Communicated by Toma Albu