Real holomorphy rings and the complete real spectrum
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. S1, pp. 57-74.

Nous introduisons la notion de spectre réel complet d’un anneau A commutatif avec unité. Les points de ce spectre réel complet, noté Sper c A, sont les triplets α=(𝔭,v,P), où 𝔭 est un idéal premier de A, v une valuation réelle du corps k(𝔭):=qf(A/𝔭) et P un ordre du corps résiduel de v. Nous montrons que Sper c A a une structure d’espace spectral au sens de Hochster [5]. On considère aussi la relation de spécialisation sur Sper c A. Nous nous intéressons particulièrement au cas où l’anneau A est un anneau d’holomorphie réel.

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 [5]. 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.

DOI : 10.5802/afst.1275
Gondard, D. 1 ; Marshall, M. 2

1 Institut de Mathématiques de Jussieu, Université Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France
2 Department of Mathematics & Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK Canada, S7N 5E6
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Gondard, D.; Marshall, M. Real holomorphy rings and the complete real spectrum. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. S1, pp. 57-74. doi : 10.5802/afst.1275. http://www.numdam.org/articles/10.5802/afst.1275/

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