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2018 | 32 | 99--131
Tytuł artykułu

The Space of Real Places on ℝ(x, y)

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The space M(ℝ (x; y)) of real places on ℝ (x; y) is shown to be path-connected. The possible value groups of these real places are determined and for each one it is shown that the set of real places with that value group is dense in the space. Large collections of subspaces of the space M(ℝ (x; y)) are constructed such that any two members of such a collection are homeomorphic. A key tool is a homeomorphism between the space of real places on ℝ((x))(y) and a certain space of sequences related to the "signatures" of [2], which themselves are shown here to be related to the "strict systems of polynomial extensions" of [3]. (original abstract)
Słowa kluczowe
PL
EN
Rocznik
Tom
32
Strony
99--131
Opis fizyczny
Twórcy
autor
  • University of Hawaii, USA
  • Soka University of America, USA
Bibliografia
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  • Engler A.J., Prestel A., Valued fields, Springer-Verlag, New York, 2005.
  • Harman J., Chains of higher level orderings, in: Dubois D.W., Recio T. (Eds.), Ordered fields and real algebraic geometry, Contemp. Math., 8, Amer. Math. Soc., Providence, 1982, pp. 141-174.
  • Kaplansky I., Maximal fields with valuations, Duke Math. J. 9 (1942), 303-321.
  • Khanduja S.K., Khassa R., On invariants and strict systems of irreducible polynomials over Henselian valued fields, Comm. Algebra 39 (2011), 584-593.
  • Knebusch M., On algebraic curves over real closed fields. I, Math. Z. 150 (1976), 49-70.
  • Kuhlmann K., The structure of spaces of R-places of rational function fields over real closed fields, Rocky Mountain J. Math. 46 (2016), 533-557.
  • Kuhlmann K., Kuhlmann F.-V., Embedding theorems for spaces of R-places of rational function fields and their products, Fund. Math. 218 (2012), 121-149.
  • Lam T.Y., Orderings, valuations and quadratic forms, CBMS Regional Conference Series in Mathematics, 52, Amer. Math. Soc., Providence, 1983.
  • MacLane S., A construction for absolute values in polynomial rings, Trans. Amer. Math. Soc. 40 (1936), 363-395.
  • Rosenstein J.G., Linear Orderings, Pure and Applied Mathematics, 98, Academic Press, New York, 1982.
  • Schülting H.-W., Real points and real places, in: Dubois D.W., Recio T. (Eds.), Ordered fields and real algebraic geometry, Contemp. Math., 8, Amer. Math. Soc., Providence, 1982, pp. 289-295.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171605653

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