of_addMonoidHom — Mathlib

English

Let p be a prime not equal to 2, and R a ring with CharP R p; then for any x ∈ R, orderOf x = 2 iff x = −1.

Русский

Пусть p — простое, p ≠ 2, и R кольцо с CharP R p; для любого x ∈ R, orderOf x = 2 тогда x = −1.

LaTeX

$$orderOf x = 2 \\\\Leftrightarrow x = -1$$

Lean4

theorem of_addMonoidHom {M N : Type*} [AddCommMonoidWithOne M] [AddCommMonoidWithOne N] [CharZero M] (e : M →+ N)
    (he : e 1 = 1) (he' : Function.Injective e) : CharZero N where
  cast_injective n m h := by rwa [← map_natCast' _ he, ← map_natCast' _ he, he'.eq_iff, Nat.cast_inj] at h

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