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Stable division rings

Published online by Cambridge University Press:  12 March 2014

Cédric Milliet
Cédric Milliet*
Affiliation:
Université de Lyon, Université Lyon 1, Institut Camille Jordan UMR 5208 CNRS, 43 Boulevard Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail: [email protected]
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Abstract

It is shown that a stable division ring with positive characteristic has finite dimension over its centre. This is then extended to simple division rings.

Keywords

Division ringstable theorysimple theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 348 - 352
Copyright
Copyright © Association for Symbolic Logic 2011

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References

REFERENCES

[1]Baldwin, John and Saxl, Jan, Logical stability in group theory, Journal of the Australian Mathematical Society, vol. 21 (1976), no. 3, pp. 267–276.CrossRefGoogle Scholar
[2]Cherlin, Gregory, Super stable division rings, Logic Colloquium '77 (Macintyre, Angus, Pacholski, Leszek, and Paris, Jeff, editors), North Holland, 1978, pp. 99–111.CrossRefGoogle Scholar
[3]Cherlin, Gregory and Shelah, Saharon, Superstable fields and groups, Annals of Mathematical Logic, vol. 18 (1980), no. 3, pp. 227–270.CrossRefGoogle Scholar
[4]Cohn, Paul M., Skew fields constructions, Cambridge University Press, 1977.Google Scholar
[5]Herstein, Israel N., Noncommutative rings, fourth ed., The Mathematical Association of America, 1996.Google Scholar
[6]Hrushovski, Ehud, On superstable fields with automorphisms, The model theory of groups, Notre Dame Mathematical Lectures, vol. 11, 1989, pp. 186–191.Google Scholar
[7]Kaplan, Itay, Scanlon, Thomas, and Wagner, Frank O., Artin-Schreier extensions in dependent and simple fields, to be published.Google Scholar
[8]Macintyre, Angus, On ω1-categorical theories of fields, Fundamenta Mathematicae, vol. 71 (1971), no. 1, pp. 1–25.CrossRefGoogle Scholar
[9]Pillay, Anand, Scanlon, Thomas, and Wagner, Frank O., Supersimple fields and division rings, Mathematical Research Letters, vol. 5 (1998), pp. 473–483.CrossRefGoogle Scholar
[10]Poizat, Bruno, Groupes stables, Nur Al-Mantiq Wal-Ma'rifah, 1987.Google Scholar
[11]Scanlon, Thomas, Infinite stable fields are Artin-Schreier closed, unpublished, 1999.Google Scholar
[12]Schlichting, Günter, Operationen mit periodischen Stabilisatoren, Archiv der Matematik, vol. 34 (1980), pp. 97–99.Google Scholar
[13]Wagner, Frank O., Stable groups, Cambridge University Press, 1997.CrossRefGoogle Scholar
[14]Wagner, Frank O., Simple theories, Mathematics and its Applications, vol. 503, Kluwer Academic Publishers, Dordrecht, 2000.CrossRefGoogle Scholar