Theorems · Theorem · commutative algebra

Ideal.ramificationIdx_eq

∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
  (q : Ideal S) [q.LiesOver p] [inst_4 : q.IsPrime],
  q.ramificationIdx R =
    (Module.length (Localization.AtPrime q)
        (Localization.AtPrime q ⧸ Ideal.map (algebraMap R (Localization.AtPrime q)) p)).toNat

Defined in: Mathlib.RingTheory.RamificationInertia.Ramification
Cited by: 6 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Ideal.LiesOver Ideal.IsPrime

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites17

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
RingHomstatement · cited by 10,189
Idealstatement and proof · cited by 4,748
Algebra.algebraMapstatement and proof · cited by 4,706
HasQuotient.Quotientstatement and proof · cited by 2,301
Ideal.IsPrimestatement and proof · cited by 827
Ideal.mapstatement and proof · cited by 692
Ideal.primeComplstatement · cited by 462
Localization.AtPrimestatement and proof · cited by 299
Ideal.LiesOverstatement and proof · cited by 272
Ideal.underproof · cited by 170

Cited by6

Results whose statement or proof uses this declaration.

Ideal.ramificationIdx'_eq_ramificationIdx'proof · cited by 3
Ideal.ramificationIdx_tower'proof · cited by 2
Ideal.ramificationIdx_smulproof · cited by 2
IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdxproof · cited by 1
Ideal.sum_ramification_inertia_eq_finrank_fiberproof · cited by 1
Ideal.ramificationIdx'_eqproof · cited by 0