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2014 | 12 | 8 | 1239-1248
Tytuł artykułu

On the dimension of the space of ℝ-places of certain rational function fields

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that for every n ∈ ℕ the space M(K(x 1, …, x n) of ℝ-places of the field K(x 1, …, x n) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x 1, …, x n)) ≤ n. For n = 2 the space M(K(x 1, x 2)) has covering and integral dimensions dimM(K(x 1, x 2)) = dimℤ M(K(x 1, x 2)) = 2 and the cohomological dimension dimG M(K(x 1, x 2)) = 1 for any Abelian 2-divisible coefficient group G.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
8
Strony
1239-1248
Opis fizyczny
Daty
wydano
2014-08-01
online
2014-05-08
Twórcy
Bibliografia
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  • [11] Kuhlmann K., The structure of spaces of R-places of rational function fields over real closed fields, preprint available at http://math.usask.ca/fvk/recpap.htm
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  • [14] Lang S., Algebra, Grad. Text in Math., 221, Springer, New York, 2002 http://dx.doi.org/10.1007/978-1-4613-0041-0
  • [15] Machura M., Marshall M., Osiak K., Metrizability of the space of R-places of a real function field, Math. Z., 2010, 266(1), 237–242 http://dx.doi.org/10.1007/s00209-009-0566-z
  • [16] Marshall M., Positive Polynomials and Sums of Squares, Math. Surveys Monogr., 146, American Mathematical Society, Providence, 2008
  • [17] Schleiermacher A., On Archimedean fields, J. Geom., 2009, 92(1–2), 143–173 http://dx.doi.org/10.1007/s00022-008-2098-9
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0409-y
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