Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.Three.Units.mem
∀ {K : Type u_1} [inst : Field K] {ζ : K} (hζ : IsPrimitiveRoot ζ 3) (u : (NumberField.RingOfIntegers K)ˣ)
[inst_1 : NumberField K] [IsCyclotomicExtension {3} ℚ K], u ∈ [1, -1, ⋯.unit, -⋯.unit, ⋯.unit ^ 2, -⋯.unit ^ 2]Let u be a unit in (𝓞 K)ˣ, then u ∈ [1, -1, η, -η, η^2, -η^2].
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 327 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites46
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Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.Three.eq_one_or_neg_one_of_unit_of_congruentproof · cited by 0