Theorems · Theorem · commutative algebra
associatedPrimes.eq_singleton_of_isPrimary
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} [IsNoetherianRing R],
I.IsPrimary → associatedPrimes R (R ⧸ I) = {I.radical}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsNoetherianRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Set.extproof · cited by 2,266
- sub_zeroproof · cited by 938
- Ideal.Quotient.mkproof · cited by 610
- IsNoetherianRingstatement and proof · cited by 268
- Set.mem_singleton_iffproof · cited by 172
- Ideal.radicalstatement and proof · cited by 121
Cited by1
Results whose statement or proof uses this declaration.
- associatedPrimes.finiteproof · cited by 3