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Vladikavkazskii Matematicheskii Zhurnal, 2015, Volume 17, Number 2, Pages 32–36
(Mi vmj541)
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Artin's theorem for $f$-rings
A. G. Kusraev Southern Mathematical Institute, Vladikavkaz Science Center of the RAS, 22 Markus street, Vladikavkaz, 362027, Russia
Abstract:
The main result states that each positive polynomial $p$ in $N$ variables with coefficients in a unital Archimedean $f$-ring $K$ is representable as a sum of squares of rational functions over the complete ring of quotients of $K$ provided that $p$ is positive on the real closure of $K$. This is proved by means of Boolean valued interpretation of Artin's famous theorem which answers Hilbert's 17th problem affirmatively.
Key words:
$f$-ring, complete ring of quotients, real closure, polynomial, rational function, Artin's theorem, Hilbert 17th problem, Boolean valued representation.
Received: 16.02.2015
Citation:
A. G. Kusraev, “Artin's theorem for $f$-rings”, Vladikavkaz. Mat. Zh., 17:2 (2015), 32–36
Linking options:
https://www.mathnet.ru/eng/vmj541 https://www.mathnet.ru/eng/vmj/v17/i2/p32
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Abstract page: | 270 | Full-text PDF : | 89 | References: | 41 |
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