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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.22 no.3 Antofagasta Dec. 2003

http://dx.doi.org/10.4067/S0716-09172003000300005 

Proyecciones
Vol. 22, N o 3, pp. 237-242, December 2003.
Universidad Católica del Norte
Antofagasta - Chile

CLASSES OF FORMS WITT EQUIVALENT
TO A SECOND TRACE FORM OVER FIELDS
OF CHARACTERISTIC TWO *

ANA CECILIA DE LA MAZA
Universidad de Talca, Chile

Abstract

Let F be a field of characteristic two. We determine all non-hyperbolic
quadratic forms over F that are Witt equivalent to a second
trace form.

Mathematics Subject Classification : Primary 11 E 04; Sec-ondary
11 E 81

Key Words:Trace form, characteristic two

References

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[CP] Conner, P., Perlis, R.: A survey of trace forms of algebraic number fields, World Scientific, Singapur, (1984).

[EHP] Estes, R., Hurrelbrink, J., Perlis, R.: Total positivity and algebraic Witt classes, Comment. Math. Helvetici 60, pp. 284-290, (1985).

[KS] Krüspkeemper, M., Scharlau, W.: On trace forms of Hilbertian fields, Comment. Math. Helvetici 63, pp. 296-304, (1988).

[R] Revoy, P.: Remarques sur la forme trace, Linear and multilinear algebra 10, pp. 223-233, (1981).

[Sa1] Sah, C.H.: Symmetric bilinear forms and quadratic forms, Journal of algebra 20, pp. 144-169, (1972).

[Se] Serre, J.P.: Linvariant de Witt de la forme tr (x 2 ), Comment. Math. Helvetici 59, pp. 657-676, (1984).

[Sch] Scharlau, W.: On trace forms of algebraic number fields,Math.Zeit. 127, pp. 125-127, (1987).

[Wat] Waterhouse, W.: Scaled trace forms over number fields,Arch.Math. 47, pp. 229-231, (1986).

Received : January, 2003.

Ana Cecilia de la Maza
Instituto de Matemática y Física
Universidad de Talca
Casilla 747
Talca
e-mail : anace@inst-mat.utalca.cl


*This work was supported by Fondecyt grants N° 1010205, and by Programa formas extremas y representación de formas cuadráticas, Universidad de Talca

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