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Asymptotic theory of modules of separably closed fields

Published online by Cambridge University Press:  12 March 2014

Françoise Point
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: [email protected]
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Abstract

We consider the reduct to the module language of certain theories of fields with a non surjective endomorphism. We show in some cases the existence of a model companion. We apply our results for axiomatizing the reduct to the theory of modules of non principal ultraproducts of separably closed fields of fixed but non zero imperfection degree.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 573 - 592
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1] Blossier, T.. Sous-groupes infiniment définissables du groups additif d'un corps séparahlement clos in “Ensembles minimaux locatement modulaires”, Ph.D. thesis. Université Paris 7, 2001.Google Scholar
[2] Blum, L., Cucker, F., Shub, M., and Smale, S., Complexity and real computation, Springer-Verlag New-York Inc., 1998.CrossRefGoogle Scholar
[3] Chatzidakis, Z. and Hrushowski, E., Some asymptotic results on fields, The Bulletin of Symbolic Logic, vol. 7 (2001), p. 105. Abstract for the Logic Colloquium 2000.Google Scholar
[4] Cohn, P. M., Skew fields, Encyclopedia of mathematics and its applications, vol. 57. Cambridge University Press, 1995.Google Scholar
[5] Dellunde, P., Delon, F., and Point, F., The theory of modules of separably dosed fields 1. this Journal, vol. 67 (2002), no. 3, pp. 997–1015.Google Scholar
[6] Dellunde, P., The theory of modules of separably closed fields 2. Annals of Pure and Applied Logic, vol. 129 (2004), pp. 181–210.CrossRefGoogle Scholar
[7] Denef, J., The Diophantine problem for polynomial rings of positive characteristic, Logic Colloquium 78 (Boffa, M., van Dalen, D., and McAloon, K., editors). North-Holland Publishing Company, 1979. pp. 131–145.Google Scholar
[8] Goodreal, K. R. and Warfield, R. B. Jr., An introduction to noncommutative rings, London Mathematical Society Student Texts, vol. 16, Cambridge University Press, 1989.Google Scholar
[9] Jacobson, N., Basic algebra I, second ed., Freeman, 1985.Google Scholar
[10] Jensen, C. U. and Lenzig, H., Model theoretic algebra, Gordon and Breach Science Publishers, 1989.Google Scholar
[11] Ore, O., Theory of non-commutative polynomials, Annals of Mathematics, vol. 34 (1933), pp. 480–508.CrossRefGoogle Scholar
[12] Singer, M. and van der Put, M., Galois theory of difference equations, Lecture Notes in Mathematics, vol. 1666, Springer, 1997.Google Scholar
[13] Stenström, B., Rings of quotients, Springer-Verlag, 1975.CrossRefGoogle Scholar
[14] Ziegler, M., Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149–213.CrossRefGoogle Scholar