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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.22 no.2 Antofagasta Aug. 2003

http://dx.doi.org/10.4067/S0716-09172003000200001 

Proyecciones
Vol. 22, N o 2, pp. 103-116, August 2003.
Universidad Católica del Norte
Antofagasta - Chile

GENERALIZATION OF THE SECOND
TRACE FORM OF CENTRAL SIMPLE
ALGEBRAS IN CHARACTERISTIC TWO*

Ana Cecilia de la Maza
Universidad de Talca, Chile

Abstract

Let F be a field with characteristic two. We generalize the second
trace form for central simple algebras with odd degree over F. We
determine the second trace form and the Arf invariant and Clifford
invariant for tensor products of central simple algebras.

Subjclass : Primary 11E04; Secondary 11E81.

Keywords trace form : Characteristic two, central simple algebras

References

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[BM] Berg´e, A. M., Martinet, J. : Formes quadratiques et extensions en caract´eristique 2, S´em. Th´eorie des Nombres de Bordeaux, expos´e 35, pp. 1- 21.(1982=83).        [ Links ]

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[M]de la Maza, A. C. : Classes of forms Witt equivalent to a second trace form over fields of characteristic two (to appear).        [ Links ]

[P]Pierce, P. : Associative Algebra, Graduate Texts in Mathematics, vol. 88, Springer-Verlag, New York (1982).        [ Links ]

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

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[T] Tignol, J. P. : La norme des espaces quadratiques et la forme trace des alg`ebres simples centrales, Pub. Math. de Besan¸con, Th´eorie des nombres, (92/93-93/94).        [ Links ]

Received : March, 2003.

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


*This work was supported by Fondecyt grants No 1010205, and by Programa formas extremas y representaci´ on de formas cuadr´ aticas, Universidad de Talca

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