SK1 of Azumaya algebras over hensel pairs

Abstract

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 SK 1 (A) coincides with its reduction SK 1 (A/IA). This generalizes a result of [6] to non-local Henselian rings.