Realizing central division algebras

Richard Scott Pierce and Charles Irvin Vinsonhaler

Vol. 109 (1983), No. 1, 165–177

DOI: 10.2140/pjm.1983.109.165

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 Q_p ⊗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