Theorems · Theorem · field theory

trdeg_add_eq

∀ (R : Type u_1) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Nontrivial R]
  {A : Type v} [inst_4 : CommRing A] [NoZeroDivisors A] [inst_6 : Algebra R A] [inst_7 : Algebra S A] [FaithfulSMul R S]
  [FaithfulSMul S A] [IsScalarTower R S A], Algebra.trdeg R S + Algebra.trdeg S A = Algebra.trdeg R A

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

Defined in

Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis

Cited by

1 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraNontrivialCommRingNoZeroDivisorsAlgebraAlgebraFaithfulSMulFaithfulSMulIsScalarTower