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Theorems · Theorem · commutative algebra

Submodule.inf_colon

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {N₁ N₂ : Submodule R M} {S : Set M}, (N₁ ⊓ N₂).colon S = N₁.colon S ⊓ N₂.colon S
Defined in
Mathlib.RingTheory.Ideal.Colon
Cited by
2 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringAddCommMonoidModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Submodule.IsPrimary.inf · cited by 2IsPrimary.infIdealFilter.IsTorsionQuot.inf · cited by 1IsTorsionQuot.infSet · cited by 53352SetModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidSubmodule · cited by 7192SubmoduleIdeal · cited by 4748IdealIdeal.ext · cited by 131Ideal.extSubmodule.colon · cited by 80Submodule.colonSubmodule.inf_colonCITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.