Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T22:59:02.259Z Has data issue: false hasContentIssue false

Totally Real Rigid Elements and Galois Theory

Published online by Cambridge University Press:  20 November 2018

Antonio José Engler*
Affiliation:
IMECC–UNICAMP Caixa Postal 6065 13083-970-Campinas-SP-Brasil email: engler@ime.unicamp.br
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Abelian closed subgroups of the Galois group of the pythagorean closure of a formally real field are described by means of the inertia group of suitable valuation rings.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1998

References

[AEJ] Arason, J.K., Elman, R. and Jacob, B., Rigid elements, valuations, and realization of Witt rings. J.Algebra 110(1987), 449467.Google Scholar
[Be] Becker, E. Hereditarily-Pythagorean Fields And Orderings Of Higher Level.Monografias de Matemètica, 29, Rio de Janeiro: IMPA 1978.Google Scholar
[Br] Bröcker, L. Characterization of fans and hereditarily Pythagorean fields. Math. Z. 151(1976), 149163.Google Scholar
[BCW] Berman, L., Cordes, C. and Ware, R., Quadratic forms, rigid elements, and formal power series fields. J. Algebra 66(1980), 123133.Google Scholar
[CR] Cordes, C. and Ramsey, J.R. Jr., Quadratic forms over fields with u = q/2 < +∞. Fund. Math. 99(1978), 110.Google Scholar
[D] Dress, A., Metrischen Ebenenüber quadratisch perfekten Körper. Math. Z. 92(1966), 1929.Google Scholar
[EL] Elman, R. and Lam, T.Y., Quadratic forms under algebraic extensions. Math. Ann. 219(1976), 2142.Google Scholar
[E] Endler, O., Valuation Theory. Berlin, Heidelberg, New York, Springer-Verlag, 1972.Google Scholar
[EE] Endler, O. and Engler, A.J., Fields with henselian valuation rings. Math. Z. 152(1977), 191193.Google Scholar
[En] Engler, A.J., Totally real rigid elements and Fô-henselian valuation rings. Comm. Algebra 25(1997), 3673.ndash;3697.Google Scholar
[EK] Engler, A.J. and Koenigsmann, J., Abelian subgroups of pro-p Galois groups. Trans. Amer.Math. Soc. 350(1998), 2473.ndash;2485.Google Scholar
[EN] Engler, A.J. and Nogueira, J.B., Maximal abelian normal subgroups of Galois pro-2-groups. J. Algebra (3) 166(1994), 481505.Google Scholar
[Gri] Griffin, M.P., The Pythagorean closure of fields. Math. Scand. 38(1976), 177191.Google Scholar
[L] Lam, T.Y., The Algebraic Theory of Quadratic Forms. New York, Benjamin, 1973.Google Scholar
[L2] Lam, T.Y., Orderings, Valuations and Quadratic Forms. Conference Board of the Mathematical Science 52,Providence, Rhode Island, Amer. Math. Soc., 1983.Google Scholar
[Schm] Schmidt, F.K., Mehrfach perfekte Körper. Math. Ann. 108(1933), 125.Google Scholar
[W] Ware, R., Valuation rings and rigid elements in fields. Canad. J. Math. 33(1981), 1338.ndash;1355.Google Scholar
[W2] Ware, R., Quadratic forms and pro 2-groups II: The Galois group of the Pythagorean closure of a formally real field. J. Pure Appl. Algebra 30(1983), 95107.Google Scholar