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Extension of orderings on $*$-fields


Author: Thomas C. Craven
Journal: Proc. Amer. Math. Soc. 124 (1996), 397-405
MSC (1991): Primary 12E15, 12J15; Secondary 16K40
DOI: https://doi.org/10.1090/S0002-9939-96-03067-5
MathSciNet review: 1301492
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Abstract: An analysis is made of the ways in which a total ordering of the set of symmetric elements of a skew field with involution can be extended to an ordering of a larger set of elements. This is done for several different types of orderings found in the literature.


References [Enhancements On Off] (What's this?)

  • Ch1 M. Chacron, c-orderable division rings with involution, J. Algebra 75 (1982), 495--522, MR 83m:16013.
  • Ch2 ------, c-valuations and normal c-orderings, Canad. J. Math. 41 (1989), 14--67, MR 90i:16016.
  • Ch3 ------, A symmetric version of the notion of c-ordering, Comm. Algebra 18 (1990), 3059--3084, MR 91g:16008.
  • Cr1 T. Craven, Orderings and valuations on $*$-fields, Rocky Mountain J. Math. 19 (1989), 629--646, MR 91j:12018a.
  • Cr2 ------, Approximation properties for orderings on $*$-fields, Trans. Amer. Math. Soc. 310 (1988), 837--850, MR 90j:12019.
  • Cr3 ------, Witt groups of hermitian forms over $*$-fields, J. Algebra 147 (1992), 96--127, MR 93d:11044.
  • Cr4 ------, Orderings, valuations and hermitian forms over $*$-fields, 1992 Summer Research Institute on Quadratic Forms and Division Algebras: Connections with Algebraic K-theory and Algebraic Geometry, Part 2, (W. Jacob and A. Rosenberg, eds.), Amer. Math. Soc., Providence, RI, 1995, pp. 149--160.
  • Da J. Dauns, A concrete approach to division rings, Heldermann Verlag, Berlin, 1982, MR 84g:16014.
  • D1 J. Dieudonné, On the structure of unitary groups, Trans. Amer. Math. Soc. 72 (1952), 367--385, MR 14:134c.
  • D2 ------, On the structure of unitary groups II, Amer. J. Math. 75 (1953), 665--678, MR 15:287f.
  • H1 S. Holland, Jr., $*$-valuations and ordered $*$-fields, Trans. Amer. Math. Soc. 262 (1980), 219--243, MR 83b:12019a.
  • H2 ------, Strong orderings of $*$-fields, J. Algebra 101 (1986), 16--46, MR 87k:12014.
  • I I. Idris, Jordan ordering of a division ring with involution, Arabian J. Sci. Engrg. 14 (1989), 527--535, MR 91e:16017.
  • MW P. Morandi and A. Wadsworth, Baer orderings with noninvariant valuation ring, Israel J. Math. 68 (1989), 241--255, MR 91c:12002.
  • O O. T. O'Meara, Introduction to Quadratic Forms, Springer-Verlag, New York, 1973, MR 50:269.

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Additional Information

Thomas C. Craven
Affiliation: Department of Mathematics, University of Hawaii at Manoa, Honolulu, Hawaii 96822-2273
Email: tom@math.hawaii.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03067-5
Keywords: Baer ordering, semiordering, $*$-ordering, valuation
Received by editor(s): July 1, 1993
Received by editor(s) in revised form: September 7, 1994
Communicated by: Lance W. Small
Article copyright: © Copyright 1996 American Mathematical Society

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