associator — Mathlib

English

For a nonunital nonassoc ring, the associator on opposite ring elements is given by a negation and opposite multiplication: associator x y z = -op (associator (unop z) (unop y) (unop x)).

Русский

Для кольца без единицы и без ассоциативности на противоположном кольце выражение associator x y z равно -op (associator (unop z) (unop y) (unop x)).

LaTeX

$$$\\text{associator}(x,y,z) = -\\mathrm{op}(\\text{associator}(\\mathrm{unop}(z),\\mathrm{unop}(y),\\mathrm{unop}(x)))$$$

Lean4

/-- The associator `(x * y) * z - x * (y * z)` -/
def associator (x y z : R) : R :=
  (x * y) * z - x * (y * z)

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