Theorems · Theorem · commutative algebra
Ideal.minimalPrimes_eq_subsingleton_self
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R} [I.IsPrime], I.minimalPrimes = {I}- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringIdeal.IsPrime
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Set.extproof · cited by 2,266
- Ideal.IsPrimestatement and proof · cited by 827
- Eq.leproof · cited by 605
- LE.le.antisymmproof · cited by 507
- Ideal.minimalPrimesstatement and proof · cited by 74
- Ideal.IsMinimalPrime.leproof · cited by 23
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.finite_minimalPrimes_of_isNoetherianRingproof · cited by 3
- Submodule.isAssociatedPrime_iffproof · cited by 1
- IsDomain.minimalPrimes_eq_singleton_botproof · cited by 1