Extending Real Valuations to Skew Polynomial Rings
نویسنده
چکیده
Let D be a division ring, T be a variable over D, σ be an endomorphism of D, δ be a σ-derivation on D and R = D[T ;σ, δ] the left skew polynomial ring over D. We show that the set (V alν(R), ) of σ-compatible real valuations which extend to R a fixed proper real valuation ν on D has a natural structure of parameterized complete non-metric tree, where is the partial order given by μ μ̃ if and only if μ(f) ≤ μ̃(f) for all f ∈ R and μ, μ̃ ∈ V alν(R).
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