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Iterated rings of bounded elements and generalizations of Schmüdgen’s Positivstellensatz. (English) Zbl 1096.13032
The author gives detailed and very elegant generalization of the result of K. Schmüdgen [Math. Ann. 289, No. 2, 203–206 (1991; Zbl 0744.44008)]. The theory developed by the author has interesting applications, e.g. he proves a conjecture of J.-P. Monnier on the equality of iterated subring of geometrically bounded elements and the subring of arithmetically bounded elements for a commutative real algebra of finite transcendence degree [Manuscr. Math. 97, No. 3, 269–302 (1998; Zbl 0922.14001)].

MSC:
13J30 Real algebra
12D15 Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
14P10 Semialgebraic sets and related spaces
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