Theorems · Theorem · commutative algebra
IsLocalization.of_le_of_exists_dvd
∀ {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] (N : Submonoid R), M ≤ N → (∀ n ∈ N, ∃ m ∈ M, n ∣ m) → IsLocalization N S- Defined in
- Mathlib.RingTheory.Localization.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsUnitproof · cited by 1,602
- IsLocalizationstatement and proof · cited by 636
- IsLocalization.map_unitsproof · cited by 69
- map_dvdproof · cited by 44
- isUnit_of_dvd_unitproof · cited by 22
- IsLocalization.of_leproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.iff_of_le_of_exists_dvdproof · cited by 1
- PrimeSpectrum.isLocalization_away_iff_atPrime_of_basicOpen_eq_singletonproof · cited by 1