Theorems · Theorem · field theory

AlgebraicIndependent.option_iff_transcendental

∀ {ι : Type u_1} {R : Type u_3} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A]
  [inst_2 : Algebra R A],
  AlgebraicIndependent R x →
    ∀ (a : A), (AlgebraicIndependent R fun o => o.elim a x) ↔ Transcendental (↥(Algebra.adjoin R (Set.range x))) a

Defined in

Mathlib.RingTheory.AlgebraicIndependent.Transcendental

Cited by

3 results in Mathlib

Foundations

Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra