Commutator automorphisms of formal power series rings

The automorphism group of a valued field of generalised formal power series

Let $ k $ be a field, $ G $ a totally ordered abelian group and $ \mathbb K = k((G)) $ the maximal field of generalised power series, endowed with the canonical valuation $ v $. We study the group $ v \mathrm{-Aut} K $ of valuation preserving automorphisms of a subfield $ k(G)\subseteq K\subseteq \mathbb K $, where $ k(G) $ is the fraction field of the group ring $ k[G] $. Under the assumption that $ K $ satisfies two lifting properties we are able to generalise and refine Hofberger's decomposition of $ v \mathrm{-Aut}\mathbb K $ and prove a structure theorem decomposing $ v\mathrm{-Aut} K $ i…

关于多变量形式幂级数逆运算算法的注记

A note on algorithmic approach to inverting multivariate formal power series

本文扩展了之前提出的多项式自同构逆运算算法，应用于任意特征域上的形式幂级数，并通过示例展示方法。