Group-graded rings and finite block theory

Yun Fan and Burkhard Külshammer

Vol. 196 (2000), No. 1, 177–186

DOI: 10.2140/pjm.2000.196.177

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.

Milestones

Received: 28 January 1999

Revised: 8 April 1999

Published: 1 November 2000