SK1 of Azumaya algebras over Hensel Pairs

Roozbeh Hazrat

doi:10.1007/s00209-008-0464-9

SK₁ of Azumaya algebras over Hensel Pairs

Roozbeh Hazrat

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

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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 SK1(A) coincides with its reduction SK1(A/I A). This generalizes a result of Hazrat (J Algebra 305:687–703, 2006) to non-local Henselian rings.

Original language	English
Pages (from-to)	295-299
Number of pages	5
Journal	Mathematische Zeitschrift
Volume	264
DOIs	https://doi.org/10.1007/s00209-008-0464-9
Publication status	Published - 19 Dec 2008

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title = "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 SK1(A) coincides with its reduction SK1(A/I A). This generalizes a result of Hazrat (J Algebra 305:687–703, 2006) to non-local Henselian rings.",

author = "Roozbeh Hazrat",

year = "2008",

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T1 - SK1 of Azumaya algebras over Hensel Pairs

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AB - 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 SK1(A) coincides with its reduction SK1(A/I A). This generalizes a result of Hazrat (J Algebra 305:687–703, 2006) to non-local Henselian rings.

U2 - 10.1007/s00209-008-0464-9

DO - 10.1007/s00209-008-0464-9

M3 - Article

SN - 0025-5874

VL - 264

SP - 295

EP - 299

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

ER -

SK1 of Azumaya algebras over Hensel Pairs

Abstract

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SK₁ of Azumaya algebras over Hensel Pairs