On formal Laurent series

被引：0

作者：

Xiao-Xiong Gan

Dariusz Bugajewski

机构：

[1] Morgan State University,Department of Mathematics

[2] Adam Mickiewicz University,Department of Mathematics and Computer Science

来源：

Bulletin of the Brazilian Mathematical Society, New Series | 2011年 / 42卷

关键词：

analytic function; composition; ℂ-algebra; formal Laurent series; formal power series; integral domain; Primary: 40A05; Secondary: 47B33, 40B05, 26E35;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Several kinds of formal Laurent series have been introduced with some restrictions so far. This paper systematically sets up a natural definition and structure of formal Laurent series without those restrictions, including introducing a multiplication between formal Laurent series. This paper also provides some results on the algebraic structure of the space of formal Laurent series, denoted by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{L}$$\end{document}. By means of the results of the generalized composition of formal power series, we define a composition of a Laurent series with a formal power series and provide a necessary and sufficient condition for the existence of such compositions. The calculus about formal Laurent series is also introduced.

引用

页码：415 / 437

页数：22

共 16 条

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