Theorems · Theorem · field theory

lift_trdeg_add_eq

∀ (R : Type u_1) (S : Type v) (A : Type w) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing A]
  [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A] [Nontrivial R]
  [NoZeroDivisors A] [FaithfulSMul R S] [FaithfulSMul S A],
  Cardinal.lift.{w, v} (Algebra.trdeg R S) + Cardinal.lift.{v, w} (Algebra.trdeg S A) =
    Cardinal.lift.{v, w} (Algebra.trdeg R A)

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

Defined in

Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTowerNontrivialNoZeroDivisorsFaithfulSMulFaithfulSMul