Theorems · Theorem · number theory
Algebra.IsUnramifiedIn.ramificationIdx_eq_one
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsDomain R]
[Module.Finite ℤ R] [CharZero R] [Algebra.EssFiniteType R S] [Algebra.IsIntegral R S] {𝔭 : Ideal R},
Algebra.IsUnramifiedIn S 𝔭 → ∀ {𝔓 : Ideal S} [𝔓.IsPrime], 𝔓.LiesOver 𝔭 → 𝔓.ramificationIdx R = 1For a prime 𝔓 of S lying over an unramified prime 𝔭 of R, the ramification index
e(𝔓 ∣ 𝔭) equals 1.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- IsDomainstatement and proof · cited by 2,196
- Module.Finitestatement and proof · cited by 1,032
- CharZerostatement and proof · cited by 932
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.LiesOverstatement and proof · cited by 272
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.EssFiniteTypestatement and proof · cited by 68
- Ideal.ramificationIdxstatement · cited by 59
- Algebra.IsUnramifiedInstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.isUnramifiedIn_iff_forall_ramificationIdx_eq_oneproof · cited by 0