On
n-associative formal power series |

Aequationes mathematicae pages 1-19, (2015). DOI 10.1007/s00010-015-0372-0

**Abstract.** A formal power series
F(x_{1},…,x_{n})∈
ℂ [[x_{1},…,x_{n}]] of order at
least 1 is called n-associative, n≥ 3, if

This notion generalizes associativity which is the special case of n=2. We determine the set of all n-associative formal power series over ℂ, all convergent n-associative power series, and all commutative (or symmetric) n-associative formal power series. Moreover we study relations between n- and m-associativity for certain n,m∈ ℕ and determine the structure of associative families (F

F(F(x _{1},…,x_{n}),x_{n+1},…,x_{2n-1})=…= F(x_{1},…,x_{n-1},F(x_{n},x_{n+1},…,x_{2n-1})).^{.}_{.}

harald.fripertinger "at" uni-graz.at, October 12, 2017

On
n-associative formal power series |