A condition on a binary operation $\cdot$ on a set $X$: that for all $x, y \in X$ $$ x \cdot (y \cdot x) = (x \cdot y) \cdot x \ . $$
In the context of non-associative rings and algebras, a flexible ring or algebra is one whose multiplication satisfies the flexible identity, which may be expressed in terms of the vanishing of the associator $(x,y,x)$.
Flexible identity. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Flexible_identity&oldid=37376