# Prüfer&#x27;s Ideal Numbers as Gelfand&#x27;s maximal Ideals - Mathematics > Number Theory

Abstract: 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 relationsbetween polyadic arithmetics and the classic theory of commutative Banachalgebras. Namely, let $\ms A$ be the algebra consisting of all complex periodicfunctions on $\Z$ with the uniform norm. Then the polyadic topological ring canbe defined as the ring of all characters $\ms A\to\C$ with convolutionoperations and the Gelfand topology.

Author: S.Albeverio, V.Polischook

Source: https://arxiv.org/