希尔伯特 17 特性和中心锥

Pub Date : 2024-10-22 DOI:10.1016/j.jalgebra.2024.10.020

Goulwen Fichou , Jean-Philippe Monnier , Ronan Quarez

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引用次数: 0

摘要

本文致力于研究一般交换环的希尔伯特 17 问题中的反蕴涵。我们引入了中心素锥和前中心素锥的概念，它们概括了不可还原实代数品种的中心实点的概念。我们研究了这些素锥族，它们都活在环的实谱中，并允许我们提出新的实在论，并获得希尔伯特第 17 个问题中的等价性。

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Hilbert 17th property and central cones

This paper is dedicated to the study of the converse implication in Hilbert 17th problem for a general commutative ring. We introduce the notions of central and precentral prime cones which generalize the notion of central real points of irreducible real algebraic varieties. We study these families of prime cones which both live in the real spectrum of the ring and allow to state new Positivstellensätze and to obtain an equivalence in Hilbert 17th problem.

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