Theorems · Theorem · commutative algebra

Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInf

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_3}
  {p : ι → Ideal R} {S : Finset ι},
  ((↑S).Pairwise fun i j => p i ⊔ p j = ⊤) →
    ⨆ i ∈ S, Submodule.torsionBySet R M ↑(p i) = Submodule.torsionBySet R M ↑(⨅ i ∈ S, p i)

Defined in

Mathlib.Algebra.Module.Torsion.Basic

Cited by

5 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModule