Theorems · Theorem · commutative algebra

Ideal.primaryComponent_sup

∀ {A : Type u_1} {M : Type u_2} [inst : CommRing A] (I : Ideal A) [inst_1 : AddCommGroup M] [inst_2 : Module A M]
  (N₁ N₂ : Submodule A M),
  Disjoint N₁ N₂ →
    Submodule.map (N₁ ⊔ N₂).subtype (Ideal.primaryComponent (↥(N₁ ⊔ N₂)) I) =
      Submodule.map N₁.subtype (Ideal.primaryComponent (↥N₁) I) ⊔
        Submodule.map N₂.subtype (Ideal.primaryComponent (↥N₂) I)

Defined in

Mathlib.Algebra.Module.Torsion.PrimaryComponent

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule