Theorems · Theorem · commutative algebra
IsAssociatedPrime.eq_radical
∀ {R : Type u_1} [inst : CommRing R] {I J : Ideal R}, I.IsPrimary → IsAssociatedPrime J (R ⧸ I) → J = I.radical- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomproof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_antisymmproof · cited by 2,068
- map_mulproof · cited by 1,137
- Ideal.IsPrimeproof · cited by 827
- Ideal.Quotient.mkproof · cited by 610
- Algebra.smul_defproof · cited by 287
Cited by1
Results whose statement or proof uses this declaration.
- associatedPrimes.eq_singleton_of_isPrimaryproof · cited by 1