Theorems · Theorem · commutative algebra

CovBy.length_baseChange

∀ {A : Type u_1} (B : Type u_2) {M : Type u_3} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : IsLocalRing A]
  [IsLocalRing B] [inst_4 : Algebra A B] [IsLocalHom (algebraMap A B)] [inst_6 : AddCommGroup M] [inst_7 : Module A M]
  [Module.Flat A B] {p q : Submodule A M},
  p ⋖ q →
    Module.length B ↥(Submodule.baseChange B q) =
      Module.length B ↥(Submodule.baseChange B p) +
        Module.length B (B ⧸ Ideal.map (algebraMap A B) (IsLocalRing.maximalIdeal A))

Defined in

Mathlib.RingTheory.LocalRing.Length

Cited by

1 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsLocalRingIsLocalRingAlgebraIsLocalHomAddCommGroupModuleModule.Flat