Associative formal power series in two indeterminates
type: Item
instance of: scholarly article
title: Associative formal power series in two indeterminates
zbMATH Open document ID: 1317.39026
author: Harald Fripertinger
author: Ludwig Reich
author: Jens Schwaiger
author: Jörg Tomaschek
published in: Semigroup Forum
publication date: 2014-09-12T00:00:00Z
full work available at URL: http://orbilu.uni.lu/handle/10993/14945
review text: A formal power series \(F\) in two variables over a commutative field \(\mathbb{K}\) is called associative if it fulfils the associativity equation \[ F(F(X, Y), Z)=F(X, F(Y, Z)). \] The authors deal with the case where \(F(X, Y)\neq X+Y+\dots \) (the case of \(F(X, Y)=X+Y+\dots \) was described by \textit{M. Hazewinkel} [Formal groups and applications. New York-San Francisco-London: Academic Press (1978; Zbl 0454.14020)]). First, they give an example of associative formal power series under consideration. Next, it is shown that the order of an associative formal power series has to be \(1\) or \(2\). Finally, a representation theorem for associative formal power series of order \(2\) (by an invertible formal power series in one variable) is provided, and the convergence of such series in the case where \(\mathbb{K}\in \{\mathbb{R}, \mathbb{C}\}\) is discussed.
reviewed by: Krzysztof Ciepliński
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 6343953
zbMATH Keywords: associativity equation
zbMATH Keywords: formal power series
zbMATH Keywords: order and convergence of associative formal power series
MaRDI profile type: Publication
OpenAlex ID: W2157935543
cites work: Q5514010
cites work: On 3-semigroups and 3-groups polynomial-derived from integral domains
cites work: Q3901604
cites work: A description of \(n\)-ary semigroups polynomial-derived from integral domains.
DOI: 10.1007/S00233-013-9533-4
Recommended article: On \(n\)-associative formal power series
Recommended article: Associative power series
Recommended article: Q4511494
Recommended article: Formal power series and Hadamard product
Recommended article: Q3774014
Recommended article: Rings of Formal Power Series in an Infinite Set of Indeterminates
Recommended article: Q3497183
Recommended article: Q5191822
Recommended article: On the summability of a class of formal power series
description: scientific article; zbMATH DE number 6343953