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Real holomorphy rings and the complete real spectrum

D. Gondard; M. Marshall — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

The complete real spectrum of a commutative ring $A$ with $1$ is introduced. Points of the complete real spectrum ${Sper}^{c} A$ are triples $α = (𝔭, v, P)$ , where $𝔭$ is a real prime of $A$ , $v$ is a real valuation of the field $k (𝔭) : = qf (A / 𝔭)$ and $P$ is an ordering of the residue field of $v$ . ${Sper}^{c} A$ is shown to have the structure of a spectral space in the sense of Hochster []. The specialization relation on ${Sper}^{c} A$ is considered. Special attention is paid to the case where the ring $A$ in question is a real holomorphy ring.

Hilbert's 17-th problem for sums of 2n-th powers.

E. Becker; R. Berr; F. Delon; D. Gondard — 1994

Journal für die reine und angewandte Mathematik

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