View source for 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}}