  A generalization of power associative algebra, called Hom-power associative
algebra, is studied. The main result says that a multiplicative Hom-algebra is
Hom-power associative if and only if it satisfies two identities of degrees
three and four. It generalizes Albert's result that power associativity is
equivalent to third and fourth power associativity. In particular,
multiplicative right Hom-alternative algebras and non-commutative Hom-Jordan
algebras are Hom-power associative.
