论文标题
正式功率系列中的功能方程
Functional equations in formal power series
论文作者
论文摘要
让$ k $是特征零的代数封闭场，而$ k [[z]] $超过$ k $的正式电源圈。在本文中，我们在Semigroup $ z^2k [[z] $中研究方程式，而半群操作为组成。我们证明了有关此类方程式的许多一般结果并提供了一些应用程序。特别是，我们回答了Horwitz和Rubel的一个问题，内容涉及``偶尔''正式力量系列的分解。我们还表明，$ z^2k [[z]] $的每个权利均为$ z^2k [z] $都与单元的半群的子集团共轭。
Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. In this paper, we study equations in the semigroup $z^2k[[z]]$ with the semigroup operation being composition. We prove a number of general results about such equations and provide some applications. In particular, we answer a question of Horwitz and Rubel about decompositions of ``even'' formal power series. We also show that every right amenable subsemigroup of $z^2k[[z]]$ is conjugate to a subsemigroup of the semigroup of monomials.
