Skip to main content
×
×
Home

Asymptotic theory of modules of separably closed fields

  • Françoise Point (a1)
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.

Copyright
References
Hide All
[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.
[2] Blum, L., Cucker, F., Shub, M., and Smale, S., Complexity and real computation, Springer-Verlag New-York Inc., 1998.
[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.
[4] Cohn, P. M., Skew fields, Encyclopedia of mathematics and its applications, vol. 57. Cambridge University Press, 1995.
[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. 9971015.
[6] Dellunde, P., The theory of modules of separably closed fields 2. Annals of Pure and Applied Logic, vol. 129 (2004), pp. 181210.
[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. 131145.
[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.
[9] Jacobson, N., Basic algebra I, second ed., Freeman, 1985.
[10] Jensen, C. U. and Lenzig, H., Model theoretic algebra, Gordon and Breach Science Publishers, 1989.
[11] Ore, O., Theory of non-commutative polynomials, Annals of Mathematics, vol. 34 (1933), pp. 480508.
[12] Singer, M. and van der Put, M., Galois theory of difference equations, Lecture Notes in Mathematics, vol. 1666, Springer, 1997.
[13] Stenström, B., Rings of quotients, Springer-Verlag, 1975.
[14] Ziegler, M., Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 149213.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×