Theorems · Theorem · commutative algebra
Submodule.isAssociatedPrime_def
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{N : Submodule R M} {I : Ideal R}, N.IsAssociatedPrime I ↔ I.IsPrime ∧ ∃ x, I = (N.colon {x}).radical- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.radicalstatement and proof · cited by 121
- Submodule.colonstatement and proof · cited by 80
- Submodule.IsAssociatedPrime.toIsPrimeproof · cited by 5
- Submodule.IsAssociatedPrimestatement and proof · cited by 5
- Submodule.IsAssociatedPrime.eq_radical_colonproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.