关于实代数几何中阿基米德正定定理的说明

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2024-09-27 DOI:10.1016/j.jpaa.2024.107811

Konrad Schmüdgen

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引用次数: 0

摘要

证明了阿基米德正定定理的一个变体，它以阿基米德半圆或生成子代数的二次模为基础。它允许人们通过更小的平方集或多项式集，获得紧凑半代数集上严格正多项式的表示。本书详细介绍了大量实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A note on the Archimedean Positivstellensatz in real algebraic geometry

A variant of the Archimedean Positivstellensatz is proved which is based on Archimedean semirings or quadratic modules of generating subalgebras. It allows one to obtain representations of strictly positive polynomials on compact semi-algebraic sets by means of smaller sets of squares or polynomials. A large number of examples is developed in detail.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.