Theorems · Theorem · commutative algebra
Localization.awayMap_surjective_iff
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] {f : R →+* S} {r : R},
Function.Surjective ⇑(Localization.awayMap f r) ↔ ∀ (a : S), ∃ b m, f b = f r ^ m * a- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Submonoid.powersstatement · cited by 408
- Localization.Awaystatement and proof · cited by 162
- Localization.awayMapstatement · cited by 33
- IsLocalization.Away.map_surjective_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.zariskisMainProperty_iffproof · cited by 3
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂proof · cited by 1
- Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐproof · cited by 1
- Localization.awayMap_awayMap_surjectiveproof · cited by 1