Right-alternative ring

Symbol-free definition
A non-associative ring (i.e., a not necessarily associative ring) is termed a right-alternative ring if it satisfies the following equivalent conditions:


 * The associator function is an alternating function of its middle and right variable.
 * The multiplicative magma of the ring is a defining ingredient::right-alternative magma.

Definition with symbols
A right-alternative ring is a non-associative ring $$R$$ (i.e., a not necessarily associative ring $$R$$) satisfying the following identity:

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

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