Theorems · Theorem · ring theory
OreLocalization.ore_eq
∀ {R : Type u_1} [inst : Monoid R] {S : Submonoid R} [inst_1 : OreLocalization.OreSet S] (r : R) (s : ↥S),
↑(OreLocalization.oreDenom r s) * r = OreLocalization.oreNum r s * ↑sThe Ore condition of a fraction, expressed in terms of oreNum and oreDenom.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- MonoidOreLocalization.OreSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement and proof · cited by 3,086
- OreLocalization.OreSetstatement and proof · cited by 92
- OreLocalization.oreNumstatement · cited by 11
- OreLocalization.oreDenomstatement · cited by 11
- OreLocalization.OreSet.ore_eqproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- OreLocalization.oreConditionproof · cited by 2
- OreLocalization.nonempty_oreSet_iff_of_noZeroDivisorsproof · cited by 1
- OreLocalization.nonempty_oreSet_iffproof · cited by 0