论文标题
代数力量系列的对角线表示：幕后一瞥
Diagonal Representation of Algebraic Power Series: A Glimpse Behind the Scenes
论文作者
论文摘要
代数功率系列有许多观点，从远程化的抽象环理论概念到作为某些有理功能的对角线的非常明确的观点。为了更明确的是，Denef和Lipshitz在1987年证明，$ N $变量中的任何代数功率系列都可以写为一个合理功率系列的对角线，其中一个变量是一个变量。他们的证明使用了许多涉及的理论和机械，这些理论和机械在原始文章中仍然隐藏给读者。在目前的工作中，我们将通过定义它们并谴责它们大部分有趣的部分来瞥见这些工具。此外，在最后一部分中，我们对Artin-Mazur引理提供了新的重大改进，证明了存在代数功率系列的二维守则。
There are many viewpoints on algebraic power series, ranging from the abstract ring-theoretic notion of Henselization to the very explicit perspective as diagonals of certain rational functions. To be more explicit on the latter, Denef and Lipshitz proved in 1987 that any algebraic power series in $n$ variables can be written as a diagonal of a rational power series in one variable more. Their proof uses a lot of involved theory and machinery which remains hidden to the reader in the original article. In the present work we shall take a glimpse on these tools by motivating while defining them and reproving most of their interesting parts. Moreover, in the last section we provide a new significant improvement on the Artin-Mazur lemma, proving the existence of a 2-dimensional code of algebraic power series.
