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Levels of division algebras

Published online by Cambridge University Press:  18 May 2009

David B. Leep
David B. Leep
Affiliation:
Department of MathematicsUniversity of KentuckyLexington KY 40506USA
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In [7] the level, sublevel, and product level of finite dimensional central division algebras D over a field F were calculated when F is a local or global field. In Theorem 1.4 of this paper we calculate the same quantities if all finite extensions K of F satisfy ū(K) ≤2, where ū is the Hasse number of a field as defined in [2]. This occurs, for example, if F is an algebraic extension of the function field R(x) where R is a real closed field or hereditarily Euclidean field (see [4]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 365 - 370
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

REFERENCES

1.Bos, R., Quadratic forms, orderings and abstract Witt rings, Dissertation (Rijksuniversiteit te Utrecht, 1984).Google Scholar
2.Elman, R., Quadratic forms and the u-invariant III, in Orzech, G., editor, Quadratic forms conference, 1976, Queen's Papers in Pure and Applied Mathematics 46 (1977), 422–444.Google Scholar
3.Elman, R. and Lam, T. Y., Quadratic forms over formally real fields and Pythagorean fields, Amer. J. Math. 94 (1972), 1155–1194.CrossRefGoogle Scholar
4.Elman, R., Lam, T. Y. and Prestel, A., On some Hasse principles over formally real fields, Math. Z. 134 (1973), 291–301.CrossRefGoogle Scholar
5.Elman, R., Lam, T. Y. and Wadsworth, A., Quadratic forms under multiquadratic extensions, Nederl. Akad. Wetensch. Indag. Math. 42 (1980), 131–145.CrossRefGoogle Scholar
6.Lam, T. Y., The algebraic theory of quadratic forms (Benjamin, 1973).Google Scholar
7.Leep, D. B., Tignol, J.-P. and Vast, N., The level of division algebras over local and global fields. J. Number. Theory 33 (1989), 53–70.CrossRefGoogle Scholar
8.Leep, D. B. and Wadsworth, A. R., The transfer ideal of quadratic forms and a Hasse norm theorem mod squares, Trans. Amer. Math. Soc. 315 (1989), 415–431.CrossRefGoogle Scholar
9.Lewis, D. W., Levels of quaternion algebras, Rocky Mountain J. Math., 19 (1989), 787–792.CrossRefGoogle Scholar
10.Lewis, D. W., Levels and sublevels of division algebras, Proc. Roy. Irish Acad. Sect. A 87 (1987), 103–106.Google Scholar
11.Scharlau, W., Quadratic forms and hermitian forms (Springer, 1985).CrossRefGoogle Scholar
12.Tignol, J.-P. and Vast, N., Représentation de –1 comme somme de carrés dans certaines algèbres de quaternions, C. R. Acad. Sci. Paris Sér. I Math. 305 (1987), 583–586.Google Scholar