Theorems · Theorem · field theory

IsTranscendenceBasis.lift_cardinalMk_eq_trdeg

∀ {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],
  IsTranscendenceBasis R x → Cardinal.lift.{w, u} (Cardinal.mk ι) = Cardinal.lift.{u, w} (Algebra.trdeg R A)

Any transcendence basis of a domain has cardinality equal to transcendental degree.

Defined in

Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis

Cited by

7 results in Mathlib

Foundations

Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraNontrivialNoZeroDivisors