Theorems · Definition · commutative algebra
Ideal.IsPrimary
{R : Type u_1} → [inst : CommSemiring R] → Ideal R → PropA proper ideal I is primary as a submodule.
- Defined in
- Mathlib.RingTheory.Ideal.IsPrimary
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Submodule.IsPrimaryproof · cited by 16
Cited by13
Results whose statement or proof uses this declaration.
- Ideal.isPrimary_iffstatement · cited by 4
- IsLocalization.under_map_of_isPrimary_disjointstatement and proof · cited by 2
- Ideal.isPrime_radicalstatement and proof · cited by 2
- Ideal.IsPrime.isPrimarystatement · cited by 2
- IsAssociatedPrime.eq_radicalstatement and proof · cited by 1
- Ideal.isPrimary_finsetInfstatement and proof · cited by 1
- associatedPrimes.eq_singleton_of_isPrimarystatement and proof · cited by 1
- Ideal.isPrimary_finset_infstatement · cited by 0
- Ideal.isPrimary_of_isMaximal_radicalstatement · cited by 0
- Ideal.IsPrimary.comapstatement and proof · cited by 0
- Ideal.IsPrimary.infstatement and proof · cited by 0
- Ideal.minimalPrimes_eq_subsingletonstatement and proof · cited by 0