Theorems · Theorem · number theory
RingOfIntegers.not_dvd_exponent_iff
∀ {K : Type u_1} [inst : Field K] {θ : NumberField.RingOfIntegers K} {p : ℕ} [Fact (Nat.Prime p)],
¬p ∣ RingOfIntegers.exponent θ ↔
Codisjoint (Ideal.comap (algebraMap ℤ (NumberField.RingOfIntegers K)) (conductor ℤ θ)) (Ideal.span {↑p})- Cited by
- 4 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Ideal.spanstatement and proof · cited by 948
- Ideal.comapstatement · cited by 443
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Codisjointstatement · cited by 197
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_spanproof · cited by 2
- RingOfIntegers.ZModXQuotSpanEquivQuotSpan_mk_applyproof · cited by 0
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_applystatement · cited by 0