Associativity of $n$-ary functions $F$ (in the sense of Post) possessing a neutral element $e$ is shown to be equivalent to the classical associativity of related binary functions $f$, so that the $F$s are the genuine $n$-ary extensions of $f$s. Based on this result, an open problem of the characterization of associative $n$-dimensional copulas is completely solved.
Reviewer: Radko Mesiar (Bratislava)