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Hasse principles and the u-invariant over formally real fields

Published online by Cambridge University Press:  22 January 2016

Roger Ware
Roger Ware*
Affiliation:
Department of Mathematics, Pennsylvania State University
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In this paper we investigate the connection between the u-invariant, u(F), of a formally real field F as defined by Elman and Lam [2] and certain Hasse Principles studied by Elman, Lam and Prestel in [3].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 117 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Elman, R. and Lam, T. Y., Quadratic forms over formally real fields and Pythagorean fields, Amer. J. Math. 94 (1972), 1155–1194.Google Scholar
[2] Elman, R. and Lam, T. Y., Quadratic forms and the u-invariant. I, Math. Z. 131 (1973), 283–304.Google Scholar
[3] Elman, R., Lam, T. Y., and Prestel, A., On some Hasse Principles over formally real fields, Math. Z. 134 (1973), 291–301.Google Scholar
[4] Gross, H. and Fischer, H. R., Non-real fields k and infinite dimensional fc-vector spaces, Math. Ann. 159 (1965), 285–308.Google Scholar
[5] Knebusch, M., Rosenberg, A., and Ware, R., Signatures on semilocal rings, J. Algebra 26 (1973), 208–250.Google Scholar
[6] Lam, T. Y., “The Algebraic Theory of Quadratic Forms”, W. A. Benjamin, Reading, Massachusetts, 1973.Google Scholar
[7] Pfister, A., Quadratische Formen in beliebigen Körpern, Invent. Math. 1 (1966), 116–132.CrossRefGoogle Scholar
[8] Prestel, A., Quadratische Semi-Ordnungen und quadratische Formen, Math. Z. 133 (1973), 319–342.CrossRefGoogle Scholar
[9] Rosenberg, A. and Ware, R., Equivalent topological properties of the space of signatures of a semilocal ring, Publ. Math. Debrecen, to appear.Google Scholar