Theorems · Theorem · group theory
Submonoid.isLocalizationMap_of_group
∀ {M : Type u_1} {G : Type u_2} [inst : CommMonoid M] [inst_1 : CommGroup G] {S : Submonoid M} {f : M → G},
Function.Injective f → (∀ (g : G), ∃ x, ∃ y ∈ S, g = f x / f y) → S.IsLocalizationMap f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidCommGroup
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- CommGroupstatement and proof · cited by 990
- div_mul_cancelproof · cited by 33
- Submonoid.IsLocalizationMapstatement · cited by 19
- Group.isUnitproof · cited by 18
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