Positivstellens\"atze for Semirings
Algebraic Geometry
2022-07-07 v1 Functional Analysis
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2207.02748,
title = {Positivstellens\"atze for Semirings},
author = {Konrad Schmüdgen and Matthias Schötz},
journal= {arXiv preprint arXiv:2207.02748},
year = {2022}
}