The Schur group of a field of characteristic zero

Richard A. Mollin

Vol. 76 (1978), No. 2, 471–478

DOI: 10.2140/pjm.1978.76.471

Abstract

We determine when a class in the Schur subgroup S(K) of the Brauer group B(K) of a field K of characteristic zero contains an algebra which is isomorphic to a simple summand A of the group algebra FG for some finite group G, where F is a subfield of K. We then investigate A ⊗_FK which is the direct sum of simple algebras with center K, and determine exactly when these are K-isomorphic. Finally we refine existing examples in the theory of the Schur group, and obtain a decomposition theorem for the related group of algebras with uniformly distributed invariants.

Mathematical Subject Classification

Primary: 12A80, 12A80

Milestones

Received: 15 July 1977

Published: 1 June 1978