Artin's theorem for $f$-rings
Автор: Kusraev Anatoly Georgievich
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.17, 2015 года.
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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.
$f$-ring, complete ring of quotients, real closure, polynomial, rational function, artin''s theorem, hilbert 17th problem, boolean valued representation
Короткий адрес: https://sciup.org/14318498
IDR: 14318498
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