On Henselian valuations and Brauer groups of primarily quasilocal fields

Abstract

This paper finds a classification, up-to an isomorphism, of abelian torsion groups realizable as Brauer groups of major types of Henselian valued primarily quasilocal fields with totally indivisible value groups. When $E$ is a quasilocal field with such a valuation, it shows that the Brauer group of $E$ is divisible and embeddable in the quotient group of the additive group of rational numbers by the subgroup of integers.