作为Gelfand极大理想的Prüfer理想数
Prüfer's Ideal Numbers as Gelfand's maximal Ideals
摘要：
多元算术是与$p$ --进理论有关的数学分支。本文的目的是说明多进算术与交换巴拿赫代数的经典理论之间有着非常密切的关系。即，设$\ms A$是由$\Z$上所有具有一致范数的复周期函数组成的代数。多进拓扑环可以定义为所有特征$\ms A\to\C$都具有卷积运算和Gelfand拓扑的环.
英文摘要：
Polyadic arithmetics is a branch of mathematics related to $p$--adic theory. The aim of the present paper is to show that there are very close relations between polyadic arithmetics and the classic theory of commutative Banach algebras. Namely, let $\ms A$ be the algebra consisting of all complex periodic functions on $\Z$ with the uniform norm. Then the polyadic topological ring can be defined as the ring of all characters $\ms A\to\C$ with convolution operations and the Gelfand topology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
