Theorems · Theorem · commutative algebra

galLift_comp

∀ {A : Type u_1} (K : Type u_2) (L : Type u_3) (L₂ : Type u_4) (L₃ : Type u_5) {B : Type u_6} {B₂ : Type u_7}
  {B₃ : Type u_8} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : CommRing B₂] [inst_3 : CommRing B₃]
  [inst_4 : Algebra A B] [inst_5 : Algebra A B₂] [inst_6 : Algebra A B₃] [inst_7 : Field K] [inst_8 : Field L]
  [inst_9 : Field L₂] [inst_10 : Field L₃] [inst_11 : Algebra A K] [inst_12 : IsFractionRing A K]
  [inst_13 : Algebra K L] [inst_14 : Algebra A L] [inst_15 : IsScalarTower A K L] [inst_16 : Algebra K L₂]
  [inst_17 : Algebra A L₂] [inst_18 : IsScalarTower A K L₂] [inst_19 : Algebra K L₃] [inst_20 : Algebra A L₃]
  [inst_21 : IsScalarTower A K L₃] [inst_22 : Algebra B L] [inst_23 : IsScalarTower A B L]
  [inst_24 : IsIntegralClosure B A L] [inst_25 : Algebra B₂ L₂] [inst_26 : IsScalarTower A B₂ L₂]
  [inst_27 : IsIntegralClosure B₂ A L₂] [inst_28 : Algebra B₃ L₃] [inst_29 : IsScalarTower A B₃ L₃]
  [inst_30 : Algebra.IsAlgebraic K L] [inst_31 : Algebra.IsAlgebraic K L₂] (σ : B →ₐ[A] B₂) (σ' : B₂ →ₐ[A] B₃),
  galLift K L L₃ (σ'.comp σ) = (galLift K L₂ L₃ σ').comp (galLift K L L₂ σ)

Defined in

Mathlib.RingTheory.IntegralClosure.IntegralRestrict

Cited by

0 results in Mathlib

Foundations

Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingCommRingAlgebraAlgebraAlgebraFieldFieldFieldFieldAlgebraIsFractionRingAlgebraAlgebraIsScalarTowerAlgebraAlgebraIsScalarTowerAlgebraAlgebraIsScalarTowerAlgebraIsScalarTowerIsIntegralClosureAlgebraIsScalarTowerIsIntegralClosureAlgebraIsScalarTowerAlgebra.IsAlgebraicAlgebra.IsAlgebraic