Consider a commutative ring R with 1. A formal power series \(F(x_1,\ldots ,x_n)\in R[\![x_1,\ldots ,x_n]\!]\) in n variables, \(n\ge 3\) , of order at least 1 is called n-associative, if the following equations \(\begin{aligned} F(F(x_1,\ldots ,x_n),x_{n+1},\ldots ,x_{2n-1})=\ldots = F(x_1,\ldots ,x_{n-1},F(x_n,x_{n+1},\ldots ,x_{2n-1})) \end{aligned}\) hold true. This notion generalizes associativity which is the special case for \(n=2\) . We describe n-associative formal power series over R. Some examples of commutative (or symmetric) n-associative formal power series are presented.
