Rocky Mountain Journal of Mathematics

Counting Generalized Orders on Not Necessarily Formally Real Fields

Ron Brown

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 35, Number 2 (2005), 401-414.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181069737

Digital Object Identifier
doi:10.1216/rmjm/1181069737

Mathematical Reviews number (MathSciNet)
MR2135576

Zentralblatt MATH identifier
1086.12003

Subjects
Primary: 12E30: Field arithmetic 12J10: Valued fields 12J12: Formally $p$-adic fields 12J15: Ordered fields

Keywords
Extended absolute value $\curlyphi$-closure $\curlyphi$-order formally $p$-adic field formally real field $\bf Z$-adic completion generalized order

Citation

Brown, Ron. Counting Generalized Orders on Not Necessarily Formally Real Fields. Rocky Mountain J. Math. 35 (2005), no. 2, 401--414. doi:10.1216/rmjm/1181069737. https://projecteuclid.org/euclid.rmjm/1181069737


Export citation

References

  • J. Ax and S. Kochen, Diophantine problems over local fields I, Amer. J. Math. 87 (1965), 605-630.
  • R. Brown, Real places and ordered fields, Rocky Mountain J. Math. 1 (1971), 633-636.
  • --------, Orders and order closures for not necessarily formally real fields, J. Algebra 169 (1994), 751-774.
  • --------, An approximation theorem for extended prime spots, Canad. J. Math. 24 (1972), 167-184.
  • --------, Extended prime spots and quadratic forms, Pacific J. Math. 51 (1974), 379-395.
  • R. Brown and J. Merzel, Rational places on algebraic function fields over generalized closed fields, J. Algebra 176 (1995), 681-701.
  • J.W.S. Cassels and A. Frölich, Algebraic number theory, Thompson Book Co., Washington, D.C., 1967.
  • L. Fuchs, Infinite Abelian groups, Vol. 1, Academic Press, New York, 1970.
  • S. Kochen, Integer valued rational functions over the $p$-adic numbers. A $p$-adic analogue of the theory of real fields, Proc. of Symposia in Pure Math., vol. 12, Number Theory, Amer. Math. Soc., Providence, RI, 1969, pp. 57-73.
  • S. Lang, The theory of real places, Ann. of Math. 57 (1953), 378-391.
  • J. Neukirch, Algebraic number theory, Springer-Verlag, Berlin, 1999.
  • A. Prestel and P. Roquette, Formally p-adic fields, Lecture Notes in Math., vol. 1050, Springer-Verlag, Berlin, 1984.
  • G. Terjanian, Un contre-exemple à une conjecture d'Artin, C.R. Acad. Sci. Paris 262 (1966), 612.
  • A. Weil, Arithmetic on algebraic varieties, Ann. of Math. 53 (1951), 412-444.