Theorems · Theorem · commutative algebra

Algebra.PreSubmersivePresentation.dimension_comp_eq_dimension_add_dimension

∀ {R : Type u} {S : Type v} {ι : Type w} {σ : Type t} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  {ι' : Type u_1} {σ' : Type u_2} {T : Type u_3} [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T]
  [inst_6 : IsScalarTower R S T] (Q : Algebra.PreSubmersivePresentation S T ι' σ')
  (P : Algebra.PreSubmersivePresentation R S ι σ) [Finite ι] [Finite ι'] [Finite σ] [Finite σ'],
  (Q.comp P).dimension = Q.dimension + P.dimension

The dimension of the composition of two finite submersive presentations is the sum of the dimensions.

Defined in

Mathlib.RingTheory.Extension.Presentation.Submersive

Cited by

1 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerFiniteFiniteFiniteFinite