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VALUED MODULES OVER SKEW POLYNOMIAL RINGS I

Published online by Cambridge University Press:  09 January 2018

GÖNENÇ ONAY
GÖNENÇ ONAY*
Affiliation:
INSTITÜT FÜR MATHEMATISCHE LOGIK UND GRUNDLAGENFORSCHUNG, FACHBEREICH UND INFORMATIK EINSTEINSTRASSE 62, 48149 MÜNSTER, GERMANYE-mail:[email protected]
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Abstract

We introduce a notion of valued module which is suitable to study valued fields of positive characteristic. Then we built-up a robust theory of henselianity in the language of valued modules and prove Ax-Kochen Ershov type results.

Keywords

Primary 03C60Secondary 03C1014G1712J2016W8013J15Ore ringsdivisible modulesp-closed fieldsvalued fieldsvalued modulesAx-Kochen and Ershov Theorem
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 4 , December 2017 , pp. 1519 - 1540
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

REFERENCES

Bélair, L. and Point, F., Quantifier elimination in valued Ore modules, this Journal, vol. 75 (2010), no. 03, pp. 1007–1034.Google Scholar
Cohn, P. M., Skew Fields: Theory of General Division Rings, Encyclopedia of Mathematics and its Applications, vol. 57, Cambridge University Press, Cambridge, 1995.Google Scholar
Dellunde, P., Delon, F., and Point, F., The theory of modules of separably closed fields 1, this Journal, vol. 67 (2002), no. 03, pp. 997–1015.Google Scholar
Delon, F., Quelques propriétés des corps valués en théorie des modèles, Thèse d’Etat, Université Paris VII, 1982.Google Scholar
Fleischer, I., Maximality and ultracompleteness in normed modules. Proceedings of the American Mathematical Society, vol. 9 (1958), no. 1, pp. 151–157.Google Scholar
Hrushovski, E. and Point, F., On von Neumann regular rings with an automorphism. Journal of Algebra, vol. 315 (2007), no. 1, pp. 76–120.Google Scholar
Jacobson, N., Basic Algebra II, second ed., W. H. Freeman and Company, New York, 1989.Google Scholar
Lam, T.-Y., Lectures on Modules and Rings, Graduate Texts in Mathematics, vol. 189, Springer-Verlag, New York, 1999.Google Scholar
Maalouf, F., Espaces vectoriels C-minimaux, this Journal, vol. 75 (2010), no. 02, pp. 741–758.Google Scholar
Marker, D., Model Theory: An Introduction, Graduate Texts in Mathematics, vol. 217, Springer-Verlag, New York, 2002.Google Scholar
Onay, G., Modules valués: en vue d’applications à la théorie des corps valués de caractéristique positive, Ph.D. thesis, Paris 7, 2011.Google Scholar
Ore, O., On a special class of polynomials. Transactions of the American Mathematical Society, vol. 35 (1933), no. 3, pp. 559–584.Google Scholar
Prest, M., Model Theory and Modules, London Mathematical Society Lecture Note Series, vol. 130, Cambridge University Press, Cambridge, 1988.Google Scholar
Rohwer, T., Valued difference fields as modules over twisted polynomial rings, Ph.D. thesis, University of Illinois at Urbana-Champaign, 2003.Google Scholar
Sabbagh, G., Sous-modules purs, existentiellement clos et élémentaires. Comptes Rendus de l’Academie des Sciences de Paris, vol. 272 (1971), no. A, pp. 1289–1292.Google Scholar
Terjanian, G., Un contre-exemple à une conjucture d’Artin. Comptes Rendus de l’Academie des Sciences de Paris, vol. 262 (1966), p. 612.Google Scholar
van den Dries, L, Classical model theory of fields, Model Theory, Algebra, and Geometry (Haskell, D., Pillay, A., and Steinhorn, C., editors), Mathematical Sciences Research Institute Publications, vol. 39, Cambridge University Press, Cambridge, 2000, pp. 37–52.Google Scholar
Kuhlmann, F. V., Additive polynomials and their role in the model theory of valued fields, Logic in Tehran, Lecture Notes in Logic, vol. 26, Association of Symbolic Logic, La Jolla, CA, 2006, pp. 160–203.Google Scholar
Whaples, G., Galois cohomology of additive polynomial and n-th power mappings of fields. Duke Mathematical Journal, vol. 24 (1957), no. 2, pp. 143–150.Google Scholar