Journal of Mathematical Sciences

, Volume 145, Issue 1, pp 4811–4817 | Cite as

Nonexcellence of certain field extensions

  • A. S. Sivatski
Article
Received:

Abstract

Towers of fields F1 ⊂ F2 ⊂ F3 are considered, where F3/F2 is a quadratic extension and F2/F1 is an extension, which is either quadratic or of odd degree or purely transcendental of degree 1. Numerous examples of the above types such that the extension F3/F1 is not 4-excellent are constructed. Also it is shown that if k is a field, char k ≠ 2, and l/k is an arbitrary field extension of fourth degree, then there exists a field extension F/k such that the fourth degree extension lF/F is not 4-excellent. Bibliography: 5 titles.

Keywords

Quadratic Form Prime Divisor Field Extension Galois Extension Hyperelliptic Curve 
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References

  1. 1.
    J. Kr. Arason, “Excellence of F()/F for 2-fold Pfister forms,” Appendix II in [2] (1977).Google Scholar
  2. 2.
    R. Elman, T. Y. Lam, and A. R. Wadsworth, “Amenable fields and Pfister extensions,” Queen’s Papers Pure Appl. Math., 46, 445–491 (1977).Google Scholar
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    M. Rost, “Quadratic forms isotropic over the function field of a conic,” Math. Ann., 288, 511–513 (1990).MATHCrossRefGoogle Scholar
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    W. Scharlau, Quadratic and Hermitian Forms, Springer, Berlin et al. (1985).MATHGoogle Scholar
  5. 5.
    A. S. Sivatski, “Nonexcellence of multiquadratic field extensions,” J. Algebra, 275, 859–866 (2004).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. S. Sivatski
    • 1
  1. 1.St. Petersburg Electrotechnical UniversitySt. PetersburgRussia

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