Theorems · Theorem · number theory

Ideal.inertiaDegIn_mul_inertiaDegIn

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (p : Ideal A)
  (P : Ideal B) [hPp : P.IsPrime] [hp : P.LiesOver p] (G : Type u_3) [inst_3 : Group G] [Finite G]
  [inst_5 : MulSemiringAction G B] [IsGaloisGroup G A B] (C : Type u_4) [inst_7 : CommRing C] [inst_8 : Algebra A C]
  [inst_9 : Algebra B C] [Nonempty ↑(P.primesOver C)] [IsScalarTower A B C] (GAC : Type u_5) [inst_12 : Group GAC]
  [Finite GAC] [inst_14 : MulSemiringAction GAC C] [IsGaloisGroup GAC A C] (GBC : Type u_6) [inst_16 : Group GBC]
  [Finite GBC] [inst_18 : MulSemiringAction GBC C] [IsGaloisGroup GBC B C],
  p.inertiaDegIn B * P.inertiaDegIn C = p.inertiaDegIn C

Defined in

Mathlib.NumberTheory.RamificationInertia.Galois

Cited by

0 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.IsPrimeIdeal.LiesOverGroupFiniteMulSemiringActionIsGaloisGroupCommRingAlgebraAlgebraNonemptyIsScalarTowerGroupFiniteMulSemiringActionIsGaloisGroupGroupFiniteMulSemiringActionIsGaloisGroup