Theorems · Theorem · commutative algebra
IsLocalization.liesOver_map_of_isPrime_disjoint
∀ {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] {I : Ideal R} [I.IsPrime],
Disjoint ↑M ↑I → (Ideal.map (algebraMap R S) I).LiesOver I- Defined in
- Mathlib.RingTheory.Localization.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingHomstatement · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- Disjointstatement and proof · cited by 2,201
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement · cited by 692
- IsLocalizationstatement and proof · cited by 636
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdxproof · cited by 1
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eqproof · cited by 1