Theorems · Theorem · commutative algebra

prod_galRestrict_eq_norm

∀ (A : Type u_1) (K : Type u_2) (L : Type u_3) (B : Type u_6) [inst : CommRing A] [inst_1 : CommRing B]
  [inst_2 : Algebra A B] [inst_3 : Field K] [inst_4 : Field L] [inst_5 : Algebra A K] [inst_6 : IsFractionRing A K]
  [inst_7 : Algebra K L] [inst_8 : Algebra A L] [inst_9 : IsScalarTower A K L] [inst_10 : Algebra B L]
  [inst_11 : IsScalarTower A B L] [inst_12 : IsIntegralClosure B A L] [inst_13 : FiniteDimensional K L]
  [inst_14 : IsGalois K L] [inst_15 : IsIntegrallyClosed A] (x : B),
  ∏ σ, ((galRestrict A K L B) σ) x =
    (algebraMap A B) (IsIntegralClosure.mk' A ((Algebra.norm K) ((algebraMap B L) x)) ⋯)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

1 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerIsIntegralClosureFiniteDimensionalIsGaloisIsIntegrallyClosed