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Theorems · Theorem · number theory

IsCyclotomicExtension.Rat.three_pid

∀ (K : Type u) [inst : Field K] [inst_1 : NumberField K] [IsCyclotomicExtension {3} ℚ K],
  IsPrincipalIdealRing (NumberField.RingOfIntegers K)

If IsCyclotomicExtension {3} ℚ K then 𝓞 K is a principal ideal domain.

Defined in
Mathlib.NumberTheory.NumberField.Cyclotomic.PID
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Foundations
Depth 316 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberFieldIsCyclotomicExtension
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Set · cited by 53352SetReal · cited by 25697RealField · cited by 7404Fieldone_mul · cited by 2841one_mulabs · cited by 1814absReal.pi · cited by 1774Real.piModule.finrank · cited by 1770Module.finrankle_of_lt · cited by 1175le_of_ltpow_one · cited by 894pow_oneneg_mul · cited by 654neg_mulNumberField · cited by 653NumberFieldne_of_gt · cited by 637ne_of_gtNat.factorial · cited by 616Nat.factorialNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersmul_pos · cited by 374mul_posRat.three_pidCITED BYCITES

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