English

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 pp--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 \msA\ms A be the algebra consisting of all complex periodic functions on Z\Z with the uniform norm. Then the polyadic topological ring can be defined as the ring of all characters \msA\C\ms A\to\C with convolution operations and the Gelfand topology.

Keywords

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}
}
R2 v1 2026-06-21T08:28:24.372Z