Theorems · Theorem · group theory
Localization.fg
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} [Monoid.FG M], S.FG → Monoid.FG (Localization S)The localization of a finitely generated monoid at a finitely generated submonoid is finitely generated.
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- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidMonoid.FG
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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
- Localizationstatement · cited by 270
- Submonoid.FGstatement and proof · cited by 24
- Monoid.FGstatement and proof · cited by 19
- Localization.mkHom_surjectiveproof · cited by 5
- Monoid.fg_of_surjectiveproof · cited by 4
- Localization.mkHomproof · cited by 3
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