Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T09:24:10.892Z Has data issue: false hasContentIssue false
  • English
  • Français

On pseudo-finite near-fields which have finite dimension over the centre

Published online by Cambridge University Press:  20 January 2009

Peter Fuchs
Peter Fuchs
Affiliation:
Institut Für MathematikJohannes Kepler Universität4040 LinzAustria
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [1] J. Ax studied a class of fields with similar properties as finite fields called pseudo-finite fields. One can prove that pseudo-finite fields are precisely the infinite models of the first-order theory of finite fields. Similarly a near-field F is called pseudo-finite if F is an infinite model of the first-order theory of finite near-fields. The structure theory of these near-fields has been initiated by U. Feigner in [5].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 371 - 375
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Ax, J., The elementary theory of finite fields, Ann. of Math. 88 (1968), 239–271.Google Scholar
2.Chang, C. C. and Keisler, H. J., Model Theory (North-Holland, Amsterdam, 1973).Google Scholar
3.Dancs, S., The sub-near-field structure of finite near-fields. Bull. Austral. Math. Soc. 5 (1971), 275–280.CrossRefGoogle Scholar
4.Dancs, S., Locally finite near-fields, Abh. Math. Sem. Univ. Hamburg 48 (1979), 89–107.Google Scholar
5.Felgner, U., Pseudo-finite near-fields (Proc. Conf. Tübingen, North-Holland, Amsterdam, 1987).CrossRefGoogle Scholar
6.Lidl, R. and Niederreiter, H., Finite Fields (Addison-Wesley, Reading, Mass., 1983).Google Scholar
7.Trautvetter, M., Planar erzeugte Fastbereiche und lineare Räume über Fastkörpern (Diss. Univ. Hamburg, 1986).Google Scholar
8.WÄhling, H., Theorie der Fastkörper (Thales Verlag, Essen, 1987).Google Scholar