Theorems · Theorem · commutative algebra
Localization.AtPrime.eq_maximalIdeal_iff_under_eq
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R} [hI : I.IsPrime] {J : Ideal (Localization.AtPrime I)},
Ideal.under R J = I ↔ J = IsLocalRing.maximalIdeal (Localization.AtPrime I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIdeal.IsPrime
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- le_antisymmproof · cited by 2,068
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapproof · cited by 692
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement and proof · cited by 299
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- Ideal.understatement and proof · cited by 170
- Ideal.IsPrime.ne_topproof · cited by 82
Cited by1
Results whose statement or proof uses this declaration.
- Localization.AtPrime.eq_maximalIdeal_iff_comap_eqproof · cited by 0