Vol. 61, No. 1, 1975

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Azumaya algebras over Hensel rings

Rosario Strano

Vol. 61 (1975), No. 1, 295–303
Abstract

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

𝒫(R) → 𝒫 (R ∕a)

is bijective.

As a corollary we obtain that, if (R,a) is an henselian couple, then the canonical homomorphism

ℬr(R) → ℬr(R∕a)

between the Brauer groups, is an isomorphism.

Mathematical Subject Classification
Primary: 13A20
Milestones
Received: 16 April 1975
Revised: 20 June 1975
Published: 1 November 1975
Authors
Rosario Strano