Theorems · Theorem · commutative algebra

galLift_algebraMap_apply

∀ {A : Type u_1} (K : Type u_2) (L : Type u_3) (L₂ : Type u_4) {B : Type u_6} {B₂ : Type u_7} [inst : CommRing A]
  [inst_1 : CommRing B] [inst_2 : CommRing B₂] [inst_3 : Algebra A B] [inst_4 : Algebra A B₂] [inst_5 : Field K]
  [inst_6 : Field L] [inst_7 : Field L₂] [inst_8 : Algebra A K] [inst_9 : IsFractionRing A K] [inst_10 : Algebra K L]
  [inst_11 : Algebra A L] [inst_12 : IsScalarTower A K L] [inst_13 : Algebra K L₂] [inst_14 : Algebra A L₂]
  [inst_15 : IsScalarTower A K L₂] [inst_16 : Algebra B L] [inst_17 : IsScalarTower A B L]
  [inst_18 : IsIntegralClosure B A L] [inst_19 : Algebra B₂ L₂] [inst_20 : IsScalarTower A B₂ L₂]
  [inst_21 : Algebra.IsAlgebraic K L] (σ : B →ₐ[A] B₂) (x : B),
  (galLift K L L₂ σ) ((algebraMap B L) x) = (algebraMap B₂ L₂) (σ x)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

4 results in Mathlib

Foundations

Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraFieldFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerIsIntegralClosureAlgebraIsScalarTowerAlgebra.IsAlgebraic