In this paper we prove the
following theorem.
Let (R,a) be an henselian couple and let 𝒫(R) be the set of isomorphism classes
of Azumaya R-algebras; then the canonical map
is bijective.
As a corollary we obtain that, if (R,a) is an henselian couple, then the canonical
homomorphism
between the Brauer groups, is an isomorphism.
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