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

Taras Banakh; Yaroslav Kholyavka; Oles Potyatynyk; Michał Machura; Katarzyna Kuhlmann

Open Mathematics (2014)

  • Volume: 12, Issue: 8, page 1239-1248
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Taras Banakh, et al. "On the dimension of the space of ℝ-places of certain rational function fields." Open Mathematics 12.8 (2014): 1239-1248. <http://eudml.org/doc/269257>.

@article{TarasBanakh2014,
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.},
author = {Taras Banakh, Yaroslav Kholyavka, Oles Potyatynyk, Michał Machura, Katarzyna Kuhlmann},
journal = {Open Mathematics},
keywords = {Space of R-places; Graphoid; Dimension; Cohomological dimension; Extension dimension; space of -places; graphoid; dimension; cohomological dimension; extension dimension},
language = {eng},
number = {8},
pages = {1239-1248},
title = {On the dimension of the space of ℝ-places of certain rational function fields},
url = {http://eudml.org/doc/269257},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Taras Banakh
AU - Yaroslav Kholyavka
AU - Oles Potyatynyk
AU - Michał Machura
AU - Katarzyna Kuhlmann
TI - On the dimension of the space of ℝ-places of certain rational function fields
JO - Open Mathematics
PY - 2014
VL - 12
IS - 8
SP - 1239
EP - 1248
AB - 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.
LA - eng
KW - Space of R-places; Graphoid; Dimension; Cohomological dimension; Extension dimension; space of -places; graphoid; dimension; cohomological dimension; extension dimension
UR - http://eudml.org/doc/269257
ER -

References

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