Theorems · Theorem · commutative algebra
Submodule.IsAssociatedPrime.toIsPrime
∀ {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- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- Submodule.IsAssociatedPrimestatement and proof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- IsAssociatedPrime.isPrimeproof · cited by 3
- IsAssociatedPrime.map_of_injectiveproof · cited by 2
- Submodule.IsMinimalPrimaryDecomposition.comap_localized₀_eq_iteproof · cited by 1
- Ideal.bot_lt_annihilator_of_disjoint_nonZeroDivisorsproof · cited by 1
- Submodule.isAssociatedPrime_defproof · cited by 0