Theorems · Theorem · commutative algebra

Algebra.rankAtStalk_eq_of_isPushout

∀ (R : Type u_3) (S : Type u_4) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (R' : Type u_5)
  (S' : Type u_6) [inst_3 : CommRing R'] [inst_4 : CommRing S'] [inst_5 : Algebra R R'] [inst_6 : Algebra S S']
  [inst_7 : Algebra R' S'] [inst_8 : Algebra R S'] [inst_9 : IsScalarTower R R' S'] [inst_10 : IsScalarTower R S S']
  [Algebra.IsPushout R S R' S'] [Module.Flat R S] [Module.Finite R S] (x : PrimeSpectrum R'),
  Module.rankAtStalk S' x = Module.rankAtStalk S (PrimeSpectrum.comap (algebraMap R R') x)

Defined in

Mathlib.RingTheory.Flat.Rank

Cited by

3 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushoutModule.FlatModule.Finite