Theorems · Theorem · field theory

AlgebraicIndependent.iff_adjoin_image

∀ {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] (s : Set ι),
  AlgebraicIndependent R x ↔
    (AlgebraicIndependent R fun i => x ↑i) ∧ AlgebraicIndepOn (↥(Algebra.adjoin R (x '' s))) x sᶜ

Defined in

Mathlib.RingTheory.AlgebraicIndependent.Transcendental

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra