Theorems · Theorem · commutative algebra
Submodule.IsPrimary.inf
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{S T : Submodule R M},
S.IsPrimary → T.IsPrimary → (S.colon Set.univ).radical = (T.colon Set.univ).radical → (S ⊓ T).IsPrimary- Defined in
- Mathlib.RingTheory.IsPrimary
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Idealstatement · cited by 4,748
- Set.univstatement and proof · cited by 3,945
- Ideal.radicalstatement and proof · cited by 121
- Submodule.colonstatement and proof · cited by 80
- inf_idemproof · cited by 37
- Submodule.IsPrimarystatement and proof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.isPrimary_finsetInfproof · cited by 2
- Ideal.IsPrimary.infproof · cited by 0