Flexible magma

This article defines a property that can be evaluated for a magma, and is invariant under isomorphisms of magmas.
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This is a variation of semigroup|Find other variations of semigroup |

Definition

A magma $(S,*)$ is termed a flexible magma if it satisfies the following identity:

$x*(y*x)=(x*y)*x\ \forall \ x,y\in S$.

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			|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			|FULL LIST, MORE INFO