# Magma in which cubes are well-defined and every element commutes with its cube

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 **magma in which cubes are well-defined and every element commutes with its cube** is a magma satisfying the following two conditions:

- For every , commutes with the value . In other words, . This common value is denoted .
- For every , .

## Relation with other properties

### Stronger properties

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

Commutative magma | any two elements commute | |FULL LIST, MORE INFO | ||

Flexible magma | flexible implies cubes are well-defined and every element commutes with its cube | |FULL LIST, MORE INFO | ||

Magma in which cubes and fourth powers are well-defined | |FULL LIST, MORE INFO | |||

Magma in which powers up to the fifth are well-defined | Magma in which cubes and fourth powers are well-defined|FULL LIST, MORE INFO |

### Weaker properties

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

Magma in which cubes are well-defined | |FULL LIST, MORE INFO |