| Title:
|
The valuated ring of the arithmetical functions as a power series ring (English) |
| Author:
|
Schwab, Emil D. |
| Author:
|
Silberberg, Gheorghe |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
77-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper examines the ring $A$ of arithmetical functions, identifying it to the domain of formal power series over ${\bf C}$ in a countable set of indeterminates. It is proven that $A$ is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that $A$ is a quasi-noetherian ring. (English) |
| Keyword:
|
arithmetical function |
| Keyword:
|
valuated ring |
| Keyword:
|
formal power series |
| MSC:
|
13F25 |
| MSC:
|
13F30 |
| idZBL:
|
Zbl 1090.13016 |
| idMR:
|
MR1822767 |
| . |
| Date available:
|
2008-06-06T22:28:26Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107789 |
| . |
| Reference:
|
[1] Bosch S., Güntzer U., Remmert R.: Non-Archimedian Analysis.Springer Verlag, 1984. MR 0746961 |
| Reference:
|
[2] Cashwell E.D., Everett C.J.: The Ring of Number-Theoretic Functions.Pacific J. Math. 9 (1959), 975–985. Zbl 0092.04602, MR 0108510 |
| Reference:
|
[3] Schwab E.D., Silberberg G.: A Note on Some Discrete Valuation Rings of Arithmetical Functions.Arch. Math. (Brno), 36 (2000), 103–109. Zbl 1058.11007, MR 1761615 |
| Reference:
|
[4] Sivaramakrishnan R.: Classical Theory of Arithmetic Functions.Monographs and Textbooks in Pure and Applied Mathematics 126, Marcel Dekker, 1989. Zbl 0657.10001, MR 0980259 |
| Reference:
|
[5] Zariski O., Samuel P.: Commutative Algebra.vol. II, Springer Verlag, 1960. Zbl 0121.27801, MR 0120249 |
| . |
