Some remarks on the stability of the Cauchy equation and completeness Publications, to be read A combinatorial approach to prove an explicit form of some iteration groups On n-associative formal power series over rings

On n-associative formal power series over rings

Jointly written with SUSAN F. EL-DEKEN.

Rendiconti del Circolo Matematico di Palermo 74, Article 24 (2025). DOI 10.1007/s12215-024-01179-0.

Abstract. Consider a commutative ring R with 1. A formal power series F(x1,…,xn)∈ R [[x1,…,xn]], in n variables, n≥ 3, of order at least 1 is called n-associative, if the following equations

F(F(x1,…,xn),xn+1,…,x2n-1)=…= F(x1,…,xn-1,F(xn,xn+1,…,x2n-1))..
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.
harald.fripertinger "at" uni-graz.at, January 12, 2026

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