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Artin's theorem for \(f\)-rings
Kusraev, A. G.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 2.
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.
Keywords: \(f\)-ring, complete ring of quotients, real closure, polynomial, rational function, Artin's theorem, Hilbert 17th problem, Boolean valued representation
Language: English Download the full text
For citation: †Kusraev A. G. Artin's theorem for \(f\)-rings. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 2, pp.32-36. DOI 10.23671/VNC.2015.2.7277
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