Theorems · Theorem · field theory

IsTranscendenceBasis.cardinalMk_eq_trdeg

∀ {R : Type u_1} {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [Nontrivial R]
  [NoZeroDivisors A] {ι : Type w} {x : ι → A}, IsTranscendenceBasis R x → Cardinal.mk ι = Algebra.trdeg R A

Defined in

Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis

Cited by

2 results in Mathlib

Foundations

Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraNontrivialNoZeroDivisors