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Mathlib.Analysis.Normed.Ring.Finite

Finite order elements in normed rings. #

A finite order element in a normed ring has norm 1.

The values of additive characters on finite cancellative monoids have norm 1.

theorem IsOfFinOrder.norm_eq_one {α : Type u_1} [NormedRing α] [NormMulClass α] [NormOneClass α] {a : α} (ha : IsOfFinOrder a) :
@[simp]
theorem AddChar.norm_apply {α : Type u_1} [NormedRing α] [NormMulClass α] [NormOneClass α] {G : Type u_3} [AddLeftCancelMonoid G] [Finite G] (ψ : AddChar G α) (x : G) :
ψ x = 1