Theorems · Theorem · field theory

AlgebraicIndependent.sumElim_of_tower

∀ {ι : Type u_1} {R : Type u_3} {S : Type u} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : CommRing A] [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A],
  AlgebraicIndependent R x →
    ∀ {ι' : Type u_4} {y : ι' → A},
      Set.range x ⊆ Set.range ⇑(algebraMap S A) → AlgebraicIndependent S y → AlgebraicIndependent R (Sum.elim y x)

Defined in

Mathlib.RingTheory.AlgebraicIndependent.Transcendental

Cited by

1 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTower