Group-graded rings and finite block theory

Abstract

Affirmative answers to two questions of Dade are given: 1. If the 1-component R1 of a ring R graded by a finite group contains only finitely many central idempotents then so does R. 2. If R is a ring fully graded by a finite group G and if S is a G-invariant unitary subring of R then, for every block idempotent a of R, the block idempotents b of S such that ab ≠ 0 form a single G-orbit.