CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Une caractérisation des corps satisfaisant le théorème de l'axe principal

  Published:1997-03-01
 Printed: Mar 1997
  • A. Movahhedi
  • A. Salinier
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Resum\'e. On caract\'erise les corps $K$ satisfaisant le th\'eor\`eme de l'axe principal \`a l'aide de propri\'et\'es des formes carac\-t\'erisation de ces m\^emes corps due \`a Waterhouse, on retrouve \`a partir de l\`a, de fa\c{c}on \'el\'ementaire, un r\'esultat de Becker selon lequel un pro-$2$-groupe qui se r\'ealise comme groupe de Galois absolu d'un tel corps $K$ est engendr\'e par des involutions. ABSTRACT. We characterize general fields $K$, satisfying the Principal Axis Theorem, by means of properties of trace forms of the finite extensions of $K$. From this and Waterhouse's characterization of the same fields, we rediscover, in quite an elementary way, a result of Becker according to which a pro-$2$-group which occurs as the absolute Galois group of such a field $K$, is generated by
MSC Classifications: 11E10, 12D15 show english descriptions Forms over real fields
Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
11E10 - Forms over real fields
12D15 - Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/