Theorems · Theorem · commutative algebra
IsLocalization.under_map_of_isPrimary_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.IsPrimary → Disjoint ↑M ↑I → Ideal.under R (Ideal.map (algebraMap R S) I) = I- Defined in
- Mathlib.RingTheory.Localization.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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 and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- mul_commproof · cited by 2,262
- Disjointstatement and proof · cited by 2,201
- le_antisymmproof · cited by 2,068
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.under_map_of_isPrime_disjointproof · cited by 15
- IsLocalization.comap_map_of_isPrimary_disjointproof · cited by 0