Theorems · Theorem · field theory

IsTranscendenceBasis.cardinalMk_eq

∀ {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] [NoZeroDivisors A] {ι' : Type u} {y : ι' → A},
  IsTranscendenceBasis R x → IsTranscendenceBasis R y → Cardinal.mk ι = Cardinal.mk ι'

[Stacks Tag 030F](https://stacks.math.columbia.edu/tag/030F)

Defined in

Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis

Cited by

1 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraNontrivialNoZeroDivisors