| Title:
|
A note on some discrete valuation rings of arithmetical functions (English) |
| Author:
|
Schwab, Emil D. |
| Author:
|
Silberberg, Gheorghe |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
103-109 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper studies the structure of the ring A of arithmetical functions, where the multiplication is defined as the Dirichlet convolution. It is proven that A itself is not a discrete valuation ring, but a certain extension of it is constructed,this extension being a discrete valuation ring. Finally, the metric structure of the ring A is examined. (English) |
| Keyword:
|
discrete valuation ring |
| Keyword:
|
arithmetical function |
| Keyword:
|
Dirichlet convolution |
| MSC:
|
11A25 |
| MSC:
|
13F30 |
| idZBL:
|
Zbl 1058.11007 |
| idMR:
|
MR1761615 |
| . |
| Date available:
|
2008-06-06T22:25:27Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107723 |
| . |
| Reference:
|
[1] Karpilovsky G.: Field theory.Marcel Dekker Inc. 1988, New York, Basel. Zbl 0677.12010, MR 0972982 |
| Reference:
|
[2] McCarthy P. J.: Regular arithmetical convolutions.Portugal. Math. 27 (1968), 1–13. Zbl 0203.35304, MR 0271015 |
| Reference:
|
[3] McCarthy P. J.: Introduction to arithmetical functions.1986, Springer-Verlag. Zbl 0591.10003, MR 0815514 |
| Reference:
|
[4] Narkiewicz W.: On a class of arithmetical convolutions.Colloq. Math. 10 (1963), 81–94. Zbl 0114.26502, MR 0159778 |
| Reference:
|
[5] Schwab E. D.: Multiplicative and additive elements in the ring of formal power series.PU.M.A. Vol. 4 (1993), 339–346. Zbl 0806.13010, MR 1283983 |
| Reference:
|
[6] Yokom K. L.: Totally multiplicative functions in regular convolution rings.Canadian Math. Bulletin 16 (1973), 119–128. MR 0325502 |
| . |
