Theorems · Theorem · number theory
RingOfIntegers.exponent_eq_one_iff
∀ {K : Type u_1} [inst : Field K] {θ : NumberField.RingOfIntegers K}, RingOfIntegers.exponent θ = 1 ↔ ℤ[θ] = ⊤- Cited by
- 2 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement and proof · cited by 535
- NumberField.RingOfIntegersstatement and proof · cited by 413
- RingOfIntegers.exponentstatement · cited by 15
- Ideal.comap_eq_top_iffproof · cited by 5
- Ideal.absNorm_eq_one_iffproof · cited by 4
- conductor_eq_top_iff_adjoin_eq_topproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvdproof · cited by 1
- IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvdproof · cited by 1