commMonoid' — Mathlib

English

If an equivalence maps x to a central element, then its image remains central.

Русский

Если отображение из класса эквивалентности переводит элемент x в центральный элемент, то его образ остаётся центральным.

LaTeX

$$∀ e, x ∈ center M, e x ∈ center N$$

Lean4

/-- The center of a multiplication with unit is commutative and associative.

This is not an instance as it forms an non-defeq diamond with `Submonoid.toMonoid` in the `npow`
field. -/
@[to_additive /-- The center of an addition with zero is commutative and associative. -/
    ]
abbrev commMonoid' : CommMonoid (center M) :=
  { (center M).toMulOneClass, Subsemigroup.center.commSemigroup with }

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