Flexible ring

Symbol-free definition
A flexible ring is a non-associative ring (i.e., a not necessarily associative ring) satisfying the following equivalent conditions:


 * 1) Its multiplication gives a defining ingredient::flexible magma.
 * 2) The associator function is alternating in its first (i.e., leftmost) and third (i.e., rightmost) variable.

Definition with symbols
A flexible ring is a non-associative ring (i.e., a not necessarily associative ring) $$R$$ satisfying:

$$x * (y * x) = (x * y) * x \ \forall \ x,y \in R$$

where $$*$$ is the multiplication in $$R$$.