Theorems · Theorem · commutative algebra
IsAssociatedPrime.isPrime
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R} {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
IsAssociatedPrime I M → I.IsPrime- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- IsAssociatedPrimestatement and proof · cited by 12
- Submodule.IsAssociatedPrime.toIsPrimeproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- IsSMulRegular.subsingleton_linearMap_iffproof · cited by 2
- Ideal.IsMaximal.mem_associatedPrimes_of_isFractionRingproof · cited by 0