Theorems · Theorem · commutative algebra
Localization.le_comap_primeCompl_iff
∀ {R : Type u_1} [inst : CommSemiring R] {P : Type u_3} [inst_1 : CommSemiring P] {I : Ideal R} [hI : I.IsPrime]
{J : Ideal P} [inst_2 : J.IsPrime] {f : R →+* P}, I.primeCompl ≤ Submonoid.comap f J.primeCompl ↔ Ideal.comap f J ≤ I- Cited by
- 10 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Submonoidstatement · cited by 3,086
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.comapstatement and proof · cited by 443
- Submonoid.comapstatement and proof · cited by 179
Cited by10
Results whose statement or proof uses this declaration.
- Localization.localRingHom_mk'statement · cited by 11
- RingHom.surjective_localRingHom_iffproof · cited by 3
- Localization.localRingHom_mkproof · cited by 3
- Algebra.weaklyQuasiFiniteAt_iffproof · cited by 2
- PrimeSpectrum.mapPiLocalization_naturalityproof · cited by 1
- AlgHom.IsArithFrobAt.isArithFrobAt_localizeproof · cited by 1
- Localization.localRingHom_bijective_of_saturated_inf_eq_topproof · cited by 1
- Localization.localRingHom_injective_of_primesOver_eq_singletonproof · cited by 1
- MaximalSpectrum.mapPiLocalization_naturalityproof · cited by 1
- AlgebraicGeometry.StructureSheaf.comap_constproof · cited by 0