Theorems · Inductive type · ring theory
OreLocalization.OreSet
{R : Type u_1} → [inst : Monoid R] → Submonoid R → Type u_1A submonoid S of a monoid R is (left) Ore if common factors on the right can be turned
into common factors on the left, and if each pair of r : R and s : S admits an Ore numerator
v : R and an Ore denominator u : S such that u * r = v * s.
- Cited by
- 92 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by128
Results whose statement or proof uses this declaration.
- OreLocalizationstatement and proof · cited by 90
- OreLocalization.oreDivstatement and proof · cited by 72
- OreLocalization.indstatement and proof · cited by 18
- OreLocalization.oreDenomstatement and proof · cited by 11
- OreLocalization.oreNumstatement and proof · cited by 11
- OreLocalization.one_defstatement and proof · cited by 10
- OreLocalization.oreDiv_eq_iffstatement and proof · cited by 9
- OreLocalization.numeratorHomstatement and proof · cited by 8
- OreLocalization.oreDiv_mul_charstatement and proof · cited by 8
- OreLocalization.oreDiv_smul_charstatement and proof · cited by 8
- OreLocalization.zero_oreDivstatement and proof · cited by 8
- OreLocalization.zero_defstatement and proof · cited by 6