\(\text{SK}_1\) of Azumaya algebras over Hensel pairs. (Q846893)

Let \(A\) be an Azumaya algebra of constant rank \(n^2\) over a Hensel pair \((R,I)\) where \(R\) is a semilocal ring with \(n\) invertible in \(R\). Then the reduced Whitehead group \(\text{SK}_1(A)\) coincides with its reduction \(\text{SK}_1(A/I A)\). This generalizes a result of \textit{R. Hazrat} [J. Algebra 305, No. 2, 687-703 (2006; Zbl 1112.16008)] to non-local Henselian rings.