Theorems · Theorem · commutative algebra

algebraMap_galRestrict_apply

∀ (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 : Algebra.IsAlgebraic K L] (σ : Gal(L/K))
  (x : B), (algebraMap B L) (((galRestrict A K L B) σ) x) = σ ((algebraMap B L) x)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

2 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerIsIntegralClosureAlgebra.IsAlgebraic