Arfs Theorem in Dimension ℵ₀

Abstract

In the whole chapter k is a field of characteristic 2 and ξ → ξ * an antiautomorphism of the field whose square is inner, ξ * * = ξ^-1 ξ ε and furthermore, ε ε * = 1 for some ε ∈ K . Let as usual S := { ξ ∈ k | ξ = ε ξ * } and T : { ξ + ε ξ * | ξ ∈ k} be the additive subgroups in k of symmetric elements and traces respectively. The factor group S/T is a k-left vector space under the composition λ ( σ + T ) = λ σ λ * + T ( σ ∈ S, λ ∈k).