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Title: On the dimension of the space of R-places of certain rational function fields
Authors: Banakh, Taras
Kholyavka, Yaroslav
Potyatynyk, Oles
Machura, Michał
Kuhlmann, Katarzyna
Keywords: space of R-places; graphoid; dimension; cohomological dimension; extension dimension
Issue Date: 2014
Citation: Central European Journal of Mathematics, Vol. 12, iss. 8, (2014), s. 1239-1248
Abstract: 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.
DOI: 10.2478/s11533-014-0409-y
ISSN: 1895-1074
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