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

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2 Citations (Scopus)

Abstract

Let A be an Azumaya algebra of constant rank n2 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
Issue number	2
DOIs	https://doi.org/10.1007/s00209-008-0464-9
Publication status	Published - 2010

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title = "SK1 of Azumaya algebras over Hensel pairs",

abstract = "Let A be an Azumaya algebra of constant rank n2 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 = "2010",

doi = "10.1007/s00209-008-0464-9",

language = "English",

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T1 - SK1 of Azumaya algebras over Hensel pairs

AU - Hazrat, Roozbeh

PY - 2010

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N2 - Let A be an Azumaya algebra of constant rank n2 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.

AB - Let A be an Azumaya algebra of constant rank n2 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.

UR - http://handle.uws.edu.au:8081/1959.7/557636

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

IS - 2

ER -

SK1 of Azumaya algebras over Hensel pairs

Abstract

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