Real holomorphy rings and the complete real spectrum

Gondard, D., and Marshall, M.. "Real holomorphy rings and the complete real spectrum." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 57-74. <http://eudml.org/doc/115903>.

@article{Gondard2010,
abstract = {The complete real spectrum of a commutative ring $A$ with $1$ is introduced. Points of the complete real spectrum $\operatorname\{Sper\}^c A$ are triples $\alpha = (\mathfrak\{p\},v,P)$, where $\mathfrak\{p\}$ is a real prime of $A$, $v$ is a real valuation of the field $k(\mathfrak\{p\}) := \operatorname\{qf\}(A/\mathfrak\{p\})$ and $P$ is an ordering of the residue field of $v$. $\operatorname\{Sper\}^c A$ is shown to have the structure of a spectral space in the sense of Hochster [5]. The specialization relation on $\operatorname\{Sper\}^c A$ is considered. Special attention is paid to the case where the ring $A$ in question is a real holomorphy ring.},
affiliation = {Institut de Mathématiques de Jussieu, Université Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France; Department of Mathematics & Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK Canada, S7N 5E6},
author = {Gondard, D., Marshall, M.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {4},
number = {S1},
pages = {57-74},
publisher = {Université Paul Sabatier, Toulouse},
title = {Real holomorphy rings and the complete real spectrum},
url = {http://eudml.org/doc/115903},
volume = {19},
year = {2010},
}

TY - JOUR
AU - Gondard, D.
AU - Marshall, M.
TI - Real holomorphy rings and the complete real spectrum
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2010/4//
PB - Université Paul Sabatier, Toulouse
VL - 19
IS - S1
SP - 57
EP - 74
AB - The complete real spectrum of a commutative ring $A$ with $1$ is introduced. Points of the complete real spectrum $\operatorname{Sper}^c A$ are triples $\alpha = (\mathfrak{p},v,P)$, where $\mathfrak{p}$ is a real prime of $A$, $v$ is a real valuation of the field $k(\mathfrak{p}) := \operatorname{qf}(A/\mathfrak{p})$ and $P$ is an ordering of the residue field of $v$. $\operatorname{Sper}^c A$ is shown to have the structure of a spectral space in the sense of Hochster [5]. The specialization relation on $\operatorname{Sper}^c A$ is considered. Special attention is paid to the case where the ring $A$ in question is a real holomorphy ring.
LA - eng
UR - http://eudml.org/doc/115903
ER -