Witt equivalence of rings of regular functions

Przemysław Koprowski

Published: 2008-09-30

Vol. 22 (2008)

Witt equivalence of rings of regular functions

Przemysław Koprowski

Abstract

In this paper we show that the rings of regular functions on two real algebraic curves over the same real closed field are Witt equivalent (i.e. their Witt rings are isomorphic) if and only if the curves have the same number of semi-algebraically connected components. Moreover, in the second part of the paper, we prove that every strong isomorphism of Witt rings of rings of regular functions can be extended to an isomorphism of Witt rings of fields of rational functions. This extension is not unique, though.

Keywords:

real algebraic curves , rings of regular functions , Witt ring of ring , Witt equivalence

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Koprowski, P. (2008). Witt equivalence of rings of regular functions. Annales Mathematicae Silesianae, 22, 45–57. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14051

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Vol. 22 (2008)
Published: 2008-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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