Power associativity

A binary operation $\star$ on a set $X$ is power associative if each element $x$ generates an associative magma: that is, exponentiation $x \mapsto x^n$ is well-defined for positive integers $n$, and $x^{m+n} = x^m \star x^n$. The set of powers of $x$ thus forms a semi-group.

See also: Algebra with associative powers.

References

• Bruck, Richard Hubert A survey of binary systems, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. 20 Springer (1958) Zbl 0081.01704