For u ∉ Q̄ and real algebraic s with s² = uū: if 1, u, ū, g, ug are free and ḡ ∈ Q̄ + Q̄u + Q̄ug, the span is Q̄ + Q̄u + Q̄ū + Q̄f + Q̄f/(s + λu) with |λ| = 1, f real

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For u ∉ Q̄ and real algebraic s with s² = uū: if 1, u, ū, g, ug are free and ḡ ∈ Q̄ + Q̄u + Q̄ug, the span is Q̄ + Q̄u + Q̄ū + Q̄f + Q̄f/(s + λu) with |λ| = 1, f real · Prove2Me