Theorems · Theorem · field theory

AlgebraicIndependent.isTranscendenceBasis_iff

∀ {ι : Type u} {R : Type u_1} {A : Type w} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [Nontrivial R],
  AlgebraicIndependent R x →
    (IsTranscendenceBasis R x ↔
      ∀ (κ : Type w) (w : κ → A), AlgebraicIndependent R w → ∀ (j : ι → κ), w ∘ j = x → Function.Surjective j)

Defined in: Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis
Cited by: 0 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Nontrivial

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