SK1 of Azumaya algebras over hensel pairs
R. Hazrat

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).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Rings, Modules, and Algebras
