Abstract
ABSTRACT Let k be a field and suppose ζn is a primitive n-th root of unity contained in k. We denote by Sr(k) = H2 (Gk,Cx) 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 (E,σζn) with the same ζn throughout. We apply this in particular to the case of a global field k and conclude by discussing the Schur multipliers of certain other types of fields.
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