# Left Bol magma with neutral element

From Groupprops

This article defines a property that can be evaluated for a magma, and is invariant under isomorphisms of magmas.

View other such properties

## Contents

## Definition

A **left Bol magma with neutral element** is a left Bol magma that has a neutral element. In other words, it is a magma such that:

- For all , we have .
- There exists , we have .

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Left Bol loop | ||||

Moufang loop |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Flexible magma | left Bol implies flexible | |||

Left alternative magma | left Bol implies left alternative |