Theorems · Theorem · commutative algebra
IsLocalization.map_under
∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) (S : Type u_2) [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [IsLocalization M S] (J : Ideal S), Ideal.map (algebraMap R S) (Ideal.under R J) = J- Defined in
- Mathlib.RingTheory.Localization.Ideal
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- le_antisymmproof · cited by 2,068
- Units.valproof · cited by 1,966
- le_rflproof · cited by 1,558
- Ideal.mapstatement and proof · cited by 692
- IsLocalizationstatement and proof · cited by 636
Cited by12
Results whose statement or proof uses this declaration.
- Localization.AtPrime.map_eq_maximalIdealproof · cited by 17
- IsLocalization.AtPrime.map_eq_maximalIdealproof · cited by 8
- IsLocalization.minimalPrimes_mapproof · cited by 4
- PrimeSpectrum.localization_comap_injectiveproof · cited by 3
- IsLocalization.isMaximal_iff_isMaximal_disjointproof · cited by 3
- Module.injective_of_isLocalizedModuleproof · cited by 2
- Ideal.IsMaximal.of_isLocalization_of_disjointproof · cited by 2
- IsLocalization.liesOver_of_isPrime_of_disjointproof · cited by 1
- isJacobsonRing_localizationproof · cited by 1
- PrimeSpectrum.localization_comap_isInducingproof · cited by 1
- IsLocalization.minimalPrimes_comapproof · cited by 1
- IsLocalization.map_comapproof · cited by 0