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The algebraic closure in function fields of quadratic forms in characteristic 2

Published online by Cambridge University Press:  17 April 2009

Hamza Ahmad
Hamza Ahmad
Affiliation:
Department of Mathematics, Yarmouk University, Irbid, Jordan
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For a field k of characteristic not two, it is known that k is algebraically closed in the function field of any (non-degenerate) quadratic form in three or more variables. In this note we consider fields of characteristic two and decide when k is algebraically closed in a function field of a quadratic k-form. For quadratic forms in three variables this has recently been done by Ohm.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 293 - 297
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Arf, C., ‘Untersuchungen über quadratische Formen in Körpern der Charakteristik 2’, J. Reine Angew Math. 183 (1941), 148–167.CrossRefGoogle Scholar
[2]Ohm, J., ‘Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski’, in Algebraic geometry and its applications, (Bajaj, C., Editor) (Springer-Verlag, Berlin, Heidelberg, New York, 1994), pp. 333–363.CrossRefGoogle Scholar
[3]Weil, A., Foundations of algebraic geometry, Amer. Math. Soc. Colloq. Publ. 29 (American Mathematical Society, Providence, RI, 1962).Google Scholar