Geodesic
Artin's theorem for $f$-rings
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 2, pp. 32-36

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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. 
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     author = {A. G. Kusraev},
     title = {Artin's theorem for $f$-rings},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
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     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a4/}
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A. G. Kusraev. Artin's theorem for $f$-rings. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 2, pp. 32-36. http://geodesic.mathdoc.fr/item/VMJ_2015_17_2_a4/