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

• Autorzy: Taras Banakh , Yaroslav Kholyavka , Oles Potyatynyk , Michał Machura , Katarzyna Kuhlmann
• 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.

Słowa kluczowe

EN

Space of R-places; Graphoid; Dimension; Cohomological dimension; Extension dimension

Kategorie tematyczne

• 12J15: Ordered fields
• 55M10: Dimension theory
• 12F20: Transcendental extensions
• 54F45: Dimension theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 8
• Strony: 1239-1248

Daty

wydano

2014-08-01

online

2014-05-08

Twórcy

autor

Taras Banakh

autor

Yaroslav Kholyavka

• Ivan Franko National University of Lviv

autor

Oles Potyatynyk

• Ivan Franko National University of Lviv

autor

Michał Machura

• University of Silesia

autor

Katarzyna Kuhlmann

• University of Silesia

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-014-0409-y