Prüfer's Ideal Numbers as Gelfand's maximal Ideals

Details Prüfer's Ideal Numbers as Gelfand's maximal Ideals Prüfer's Ideal Numbers as Gelfand's maximal Ideals

2007-05-15

arxiv.org/abs/0705.2095v1

Mathematics

Number Theory

30 pages

Scientific paper

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.

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