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Theorems · Definition · group theory

Units.ofPowEqOne

{M : Type u_1} → [inst : Monoid M] → (a : M) → (n : ℕ) → a ^ n = 1 → n ≠ 0 → Mˣ

If a ^ n = 1, n ≠ 0, then a is a unit.

Defined in
Mathlib.Algebra.Group.Commute.Units
Cited by
6 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext
Assumes
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

rootsOfUnity.mkOfPowEq · cited by 7rootsOfUnity.mkOfPowEqIsUnit.of_pow_eq_one · cited by 4IsUnit.of_pow_eq_oneUnits.val_ofPowEqOne · cited by 2Units.val_ofPowEqOneUnits.pow_ofPowEqOne · cited by 0Units.pow_ofPowEqOneautAdjoinRootXPowSubCEquiv_symm_smul · cited by 0autAdjoinRootXPowSubCEqui…invertibleOfPowEqOne · cited by 0invertibleOfPowEqOneUnits.ofPowEqOne.congr_simp · cited by 0ofPowEqOne.congr_simpUnits.val_inv_ofPowEqOne · cited by 0Units.val_inv_ofPowEqOneMonoid · cited by 3887MonoidUnits · cited by 2804UnitsUnits.ofPow · cited by 1Units.ofPowUnits.ofPowEqOneCITED BYCITES

Cites3

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Cited by8

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