# Definition:Algebra Loop

## Contents

## 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.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Exercise $7.8$