Theorems · Theorem · commutative algebra
IsLocalization.disjoint_under_iff
∀ {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), Disjoint ↑M ↑(Ideal.under R J) ↔ J ≠ ⊤- Defined in
- Mathlib.RingTheory.Localization.Ideal
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Submonoidstatement and proof · cited by 3,086
- Disjointstatement · cited by 2,201
- IsLocalizationstatement and proof · cited by 636
- Ideal.understatement and proof · cited by 170
- IsLocalization.map_unitsproof · cited by 69
- Set.not_disjoint_iffproof · cited by 30
Cited by6
Results whose statement or proof uses this declaration.
- IsLocalization.minimalPrimes_mapproof · cited by 4
- IsLocalization.AtPrime.radical_map_of_mem_minimalPrimesproof · cited by 1
- IsLocalization.disjoint_comap_iffproof · cited by 0