Vol. 109, No. 1, 1983

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Realizing central division algebras

Richard Scott Pierce and Charles Irvin Vinsonhaler

Vol. 109 (1983), No. 1, 165–177
Abstract

Let D be a finite dimensional division algebra over the rational field. We consider the question: for which primes p is D isomorphic to the quasi-endomorphism algebra of a p-local torsion free abelian group G whose rank is equal to the dimension of D? We show that D can be realized in this way for exactly those primes p such that Qp D is not a product of division algebras.

Mathematical Subject Classification 2000
Primary: 16A46, 16A46
Secondary: 20K15
Milestones
Received: 10 February 1982
Revised: 19 April 1982
Published: 1 November 1983
Authors
Richard Scott Pierce
Charles Irvin Vinsonhaler