[−][src]Trait mathru::algebra::abstr::Loop

pub trait Loop<O: Operator>: Quasigroup<O> + Identity<O> { }

A quasigroup with an unique identity element.

$\exists e \in \mathbb{Q}, \forall a \in \mathbb{Q}, \exists r, l \in \mathbb{Q}$ such that $l ∘ a = a ∘ r = e $ The left inverse $r$ and right inverse $l$ are not required to be equal. The following property is added to the quasigroup structure:

This property follows from

$\forall a \in \mathbb{Q}, \exists e \in \mathbb{Q}$, such that $e ∘ a = a ∘ e = a$.