Theorems · Theorem · group theory
Localization.mk_pow
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} (n : ℕ) (a : M) (b : ↥S),
Localization.mk a b ^ n = Localization.mk (a ^ n) (b ^ n)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
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.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Localizationstatement · cited by 270
- Commute.allproof · cited by 119
- Localization.mkstatement · cited by 110
- OreLocalization.oreDiv_powproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.val_powproof · cited by 4
- HomogeneousLocalization.awayMapAux_mkproof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- HomogeneousLocalization.Away.finiteTypeproof · cited by 0