Original Articles

ON A CONNECTION BETWEEN THE SCHUR MULTIPLIER AND THE BRAUER GROUP OF A FIELD

Published in: Quaestiones Mathematicae
Volume 9 , issue 1-4 , 1986 , pages: 349–362

DOI: 10.1080/16073606.1986.9632122

Author(s): Falko Lorenz Mathematisches Institut, Federal Republic of Germany

Abstract

Let k be a field and suppose ζ_n is a primitive n-th root of unity contained in k. We denote by Sr(k) = H² (G_k,C^x) the Schur multiplier of k. We observe: If the n-part of Sr(k) is trivial, then every element of order n in the Brauer group Br(k) can be represented as a cyclic algebra of the form

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