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arXiv · 2207.02748

Positivstellens\"atze for Semirings

Konrad Schmüdgen·Matthias Schötz
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Abstract

In this paper we develop a number of results and notions concerning Positivstellens\"atze for semirings (preprimes) of commutative unital real algebras. First we reduce the Archimedean Positivstellensatz for semirings to the corresponding result for quadratic modules. Various applications of the Archimedean Positivstellensatz for semirings are investigated. A general Positivstellensatz with denominators is proved for filtered algebras with semirings. As an application we derive a denominator-free Positivstellensatz for the cylindrical extension of an algebra with Archimedean semiring. A large number of illustrating examples are given.

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BibTeXRIS

Konrad Schmüdgen, Matthias Schötz. 2022-07-06. Positivstellens\"atze for Semirings. https://arxiv.org/abs/2207.02748

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