Theorems · Theorem · ring theory
OreLocalization.numeratorHom_inj
∀ {R : Type u_1} [inst : Ring R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S],
S ≤ nonZeroDivisorsLeft R → Function.Injective ⇑OreLocalization.numeratorHom- Defined in
- Mathlib.RingTheory.OreLocalization.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Quot.sound
- Assumes
- RingOreLocalization.OreSet
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.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- mul_oneproof · cited by 3,885
- MonoidHomstatement · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- sub_eq_zeroproof · cited by 407
- mul_subproof · cited by 201
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivproof · cited by 72
- nonZeroDivisorsLeftstatement and proof · cited by 26
- OreLocalization.oreDiv_eq_iffproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- OreLocalization.cardinalMkproof · cited by 1