# Flexible magma

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

This is a variation of semigroup|Find other variations of semigroup |

## Contents

## Definition

A magma is termed a **flexible magma** if it satisfies the following identity:

.

## Relation with other properties

### Stronger properties

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

Diassociative magma | submagma generated by any two elements is associative | |FULL LIST, MORE INFO | ||

Semigroup | Associativity holds universally | Diassociative magma|FULL LIST, MORE INFO | ||

Commutative magma | Commutativity holds universally | |FULL LIST, MORE INFO | ||

Flexible loop | loop that is flexible as a magma | |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 | every element commutes with its square | Magma in which cubes are well-defined and every element commutes with its cube|FULL LIST, MORE INFO |