| Title:
|
A completion of $\mathbb{Z}$ is a field (English) |
| Author:
|
Marcos, J. E. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
689-706 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
sequential convergence |
| Keyword:
|
convergence ring |
| Keyword:
|
completion of a convergence ring |
| MSC:
|
13J10 |
| MSC:
|
13J99 |
| MSC:
|
54A20 |
| MSC:
|
54H13 |
| idZBL:
|
Zbl 1080.54500 |
| idMR:
|
MR2000063 |
| . |
| Date available:
|
2009-09-24T11:05:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127833 |
| . |
| Reference:
|
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