Prüfer's Ideal Numbers as Gelfand's maximal Ideals

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 comple...

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Bibliographic Details
Published in:arXiv.org 2007-05
Main Authors: Albeverio, S, Polischook, V
Format: Article
Language:English
Subjects:
Convolution
Periodic functions
Rings (mathematics)
Topology
Online Access:Get full text
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Summary: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.
ISSN:2331-8422