SK1 of Azumaya algebras over hensel pairs

TL;DR

This paper proves that for Azumaya algebras over hensel pairs with certain conditions, the reduced Whitehead group SK(A) equals SK(A/IA), simplifying its computation.

Contribution

It establishes the equality of SK(A) and SK(A/IA) for Azumaya algebras over hensel pairs, extending understanding of Whitehead groups in algebraic K-theory.

Findings

SK(A) equals SK(A/IA) under given conditions

Simplifies calculations of Whitehead groups for Azumaya algebras

Provides new insight into algebraic K-theory 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(A) coincides with its reduction SK(A/IA).