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

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Banakh T., Kholyavka Y., Potyatynyk O., Machura M., Kuhlmann K.

Open Mathematics

2014

tom 12

nr 8

1239-1248

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.

Ograniczanie wyników

1 Open Mathematics

1 Banakh T.

1 Kholyavka Y.

1 Kuhlmann K.

1 Machura M.

1 Potyatynyk O.

1 2014

Wyniki wyszukiwania

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