Vol. 76, No. 2, 1978

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The Schur group of a field of characteristic zero

Richard A. Mollin

Vol. 76 (1978), No. 2, 471–478

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
Received: 15 July 1977
Published: 1 June 1978
Richard A. Mollin
Department of Mathematics and Statistics
University of Calgary
Calgary T2N 1N4