Theorems · Theorem · commutative algebra

Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicity

∀ {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) [IsDedekindDomain S] [q.IsPrime] [q.LiesOver p],
  Ideal.map (algebraMap R S) p ≠ ⊥ → q.ramificationIdx R = multiplicity q (Ideal.map (algebraMap R S) p)

Defined in

Mathlib.RingTheory.RamificationInertia.Ramification

Cited by

2 results in Mathlib

Foundations

Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIsDedekindDomainIdeal.IsPrimeIdeal.LiesOver