Hostname: page-component-6bf8c574d5-r4mrb Total loading time: 0 Render date: 2025-03-07T02:39:46.707Z Has data issue: false hasContentIssue false
  • English
  • Français

The theory of modules of separably closed fields 1

Published online by Cambridge University Press:  12 March 2014

Pilar Dellunde ,
Françoise Delon  and
Françoise Point
Pilar Dellunde
Affiliation:
Àrea de Lògica, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain, E-mail: Pilar.Dellunde@uab.es
Françoise Delon
Affiliation:
C.N.R.S., U.P.R.E.S.A.7056 et Université Paris 7, U.F.R. de Mathématiques, Case 7012, 2 Place Jussieu, 75251 Paris Cedex 5, France, E-mail: delon@logique.jussieu.fr
Françoise Point
Affiliation:
Institut de Mathématique et Informatique, Université de Mons-Hainaut, Le Pentagone, 6, Avenue du Champ de Mars, B-7000 Mons, Belgium, E-mail: point@logique.jussieu.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider separably closed fields of characteristic p > 0 and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the p-component functions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 997 - 1015
Copyright
Copyright © Association for Symbolic Logic 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Blossier, T., Sous-groupes infiniment définissables du groupe additif d'un corps séparablement clos, in “Ensembles minimaux localement modulaires”, thèse de doctorat, Université Paris 7, 2001.Google Scholar
[2]Cohn, P. M., Skew fields, Encyclopedia of mathematics and its applications (Rota, G.-C., editor), vol. 57, Cambridge University Press, 1995.Google Scholar
[3]Dellunde, P., Delon, F., and Point, F., The theory of modules of separably closed fields-2, preprint.Google Scholar
[4]Delon, F., Idéaux et types sur les corps séparablement clos, Supplément au Bulletin de la Société Mathématique de France, (1988), Mémoire 33, Tome116.Google Scholar
[5]Ershov, Y., Fields with a solvable theory, Doklady, vol. 174 (1967), pp. 19–20, English translation in Soviet Mathematics vol. 8, pp. 575–576, 1967.Google Scholar
[6]Jacobson, N., Basic algebra I, second ed., Freeman, 1985.Google Scholar
[7]Martin, G. A., Definability in reducts of algebraically closed fields, this Journal, vol. 53 (1988), pp. 188–199.Google Scholar
[8]Ore, O., On a special class of polynomials, Transactions of the American Mathematical Society, vol. 35 (1933), pp. 559–584.CrossRefGoogle Scholar
[9]Ore, O., Theory of non-commutative polynomials, Annals of Mathematics, vol. 34 (1933), pp. 480–508.CrossRefGoogle Scholar
[10]Prest, M., Model theory and modules, London Mathematical Society Lecture Notes Series, vol. 130 (1988), Cambridge University Press.Google Scholar
[11]Wood, C., Notes on the stability of separably closed fields, this Journal, vol. 44 (1979), pp. 412–416.Google Scholar
[12]Ziegler, M., Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149–213.CrossRefGoogle Scholar