Theorems · Theorem · number theory
IsPrimitiveRoot.finite_quotient_toInteger_sub_one
∀ {K : Type u} [inst : Field K] {ζ : K} [NumberField K] {k : ℕ} (hk : 1 < k) (hζ : IsPrimitiveRoot ζ k),
Finite (NumberField.RingOfIntegers K ⧸ Ideal.span {hζ.toInteger - 1})𝓞 K ⧸ Ideal.span {ζ - 1} is finite.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldNumberField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Idealstatement · cited by 4,748
- Bot.botproof · cited by 4,720
- Finitestatement · cited by 3,029
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.spanstatement and proof · cited by 948
- NumberFieldstatement and proof · cited by 653
- NumberField.RingOfIntegersstatement · cited by 413
- IsPrimitiveRootstatement and proof · cited by 356
- IsPrimitiveRoot.toIntegerstatement and proof · cited by 72
- NumberField.RingOfIntegers.ext_iffproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_oneproof · cited by 2