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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On quadratic forms over semilocal rings


Author: Stefan Gille
Journal: Trans. Amer. Math. Soc. 371 (2019), 1063-1082
MSC (2010): Primary 11E81; Secondary 11E88
DOI: https://doi.org/10.1090/tran/7270
Published electronically: July 26, 2018
MathSciNet review: 3885171
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Abstract: Using a recent result of Panin and Pimenov we show that several results, as for instance the linkage principle, in the algebraic theory of quadratic forms over fields also hold for quadratic forms over regular semilocal domains which contain a field of characteristic not 2. As an application we prove that the Arason and Elman presentation of the powers of the fundamental ideal of the Witt ring of a field extends to semilocal rings which contain an infinite field of characteristic not 2.


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Additional Information

Stefan Gille
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: gille@ualberta.ca

DOI: https://doi.org/10.1090/tran/7270
Keywords: Quadratic forms, (semi-)local rings, Witt groups
Received by editor(s): June 26, 2015
Received by editor(s) in revised form: February 3, 2017, and April 5, 2017
Published electronically: July 26, 2018
Additional Notes: This work was supported by an NSERC grant.
Article copyright: © Copyright 2018 American Mathematical Society