# Definition:Algebra Loop

## Definition

An algebra loop $\left({S, \circ}\right)$ is a quasigroup with an identity element.

That is:

$\exists e \in S: \forall x \in S: x \circ e = x = e \circ x$.

## Also known as

Some sources refer to an algebra loop as just a loop.

## Also see

• Results about algebra loops can be found here.