Flexible algebra

Summary

A flexible algebra is a nonassociative algebra in which $(xy)x = x(yx)$ for all elements $x, y$. So the expression $xyx$ has one meaning, whatever the bracketing. All associative, all commutative and all anticommutative algebras are flexible, and so are all alternative algebras. Flexibility is a weak replacement for associativity that still allows a good structure theory.