Theorems · Definition · ring theory
OreLocalization.numeratorRingHom
{R : Type u_1} →
[inst : Semiring R] → {S : Submonoid R} → [inst_1 : OreLocalization.OreSet S] → R →+* OreLocalization S RThe ring homomorphism from R to R[S⁻¹], mapping r : R to the fraction r /ₒ 1.
- Defined in
- Mathlib.RingTheory.OreLocalization.Ring
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Quot.sound
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.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- MonoidHomproof · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.numeratorHomproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- RingHom.locally_respectsIsoproof · cited by 1
- OreLocalization.numeratorRingHom_applystatement and proof · cited by 0