Theorems · Definition · group theory
Submonoid.powers
{M : Type u_1} → [inst : Monoid M] → M → Submonoid MThe submonoid generated by an element.
- Cited by
- 408 results in Mathlib
- Foundations
- Depth 24 from the axioms, rests on 284 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.rangeproof · cited by 4,705
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- MonoidHom.mrangeproof · cited by 63
- powersHomproof · cited by 6
- Submonoid.copyproof · cited by 4
Cited by470
Results whose statement or proof uses this declaration.
- IsLocalization.Awayproof · cited by 218
- Localization.Awayproof · cited by 162
- HomogeneousLocalization.Awayproof · cited by 105
- Localization.awayMapstatement · cited by 33
- AlgebraicGeometry.Proj.awayιstatement · cited by 30
- IsLocalizedModule.Awayproof · cited by 27
- HomogeneousLocalization.awayMapstatement · cited by 27
- LocalizedModule.Awayproof · cited by 20
- Submonoid.powers_lestatement · cited by 19
- AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpenproof · cited by 18
- PrimeSpectrum.localization_away_comap_rangeproof · cited by 17
- AlgebraicGeometry.Scheme.Hom.ker_applyproof · cited by 14
Showing the 200 most cited of 470.