Theorems · Theorem · field theory

AlgebraicIndependent.isEmpty_of_isAlgebraic

∀ {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 → ∀ [Algebra.IsAlgebraic R A], IsEmpty ι

If A/R is algebraic, then all algebraically independent families are empty.

Defined in

Mathlib.RingTheory.AlgebraicIndependent.Transcendental

Cited by

2 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAlgebra.IsAlgebraic