Pr\"ufer's Ideal Numbers as Gelfand's maximal Ideals
Number Theory
2007-05-23 v1 Functional Analysis
Abstract
Polyadic arithmetics is a branch of mathematics related to --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 be the algebra consisting of all complex periodic functions on with the uniform norm. Then the polyadic topological ring can be defined as the ring of all characters with convolution operations and the Gelfand topology.
Cite
@article{arxiv.0705.2095,
title = {Pr\"ufer's Ideal Numbers as Gelfand's maximal Ideals},
author = {S. Albeverio and V. Polischook},
journal= {arXiv preprint arXiv:0705.2095},
year = {2007}
}