An algebra in which the associator 
.
The subalgebra generated by one element is associative.
Power Associative Algebra
See also
AssociatorExplore with Wolfram|Alpha
References
Schafer, R. D. An Introduction to Non-Associative Algebras. New York: Dover, 1995.Referenced on Wolfram|Alpha
Power Associative AlgebraCite this as:
Weisstein, Eric W. "Power Associative Algebra." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PowerAssociativeAlgebra.html