A completion of $\mathbb{Z}$ is a field

Title:

A completion of $\mathbb{Z}$ is a field

Creator:

Marcos, José E.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3920a41a-5f1e-41ca-90b0-580c1b582163
uuid:3920a41a-5f1e-41ca-90b0-580c1b582163

Subject:

sequential convergence, convergence ring, and completion of a convergence ring

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We define various ring sequential convergences on $\mathbb{Z}$ and $\mathbb{Q}$. We describe their properties and properties of their convergence completions. In particular, we define a convergence $\mathbb{L}_1$ on $\mathbb{Z}$ by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields $\mathbb{Z}/(p)$. Further, we show that $(\mathbb{Z}, \mathbb{L}^\ast _1)$ is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

689-706

Source:

Czechoslovak Mathematical Journal | 2003 Volume:53 | Number:3

Harvested from:

CDK

Metadata only:

false