# A note on some discrete valuation rings of arithmetical functions

Emil Daniel Schwab; Gheorghe Silberberg

Archivum Mathematicum (2000)

- Volume: 036, Issue: 2, page 103-109
- ISSN: 0044-8753

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topSchwab, Emil Daniel, and Silberberg, Gheorghe. "A note on some discrete valuation rings of arithmetical functions." Archivum Mathematicum 036.2 (2000): 103-109. <http://eudml.org/doc/248540>.

@article{Schwab2000,

abstract = {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.},

author = {Schwab, Emil Daniel, Silberberg, Gheorghe},

journal = {Archivum Mathematicum},

keywords = {discrete valuation ring; arithmetical function; Dirichlet convolution; discrete valuation ring; arithmetical function; Dirichlet convolution},

language = {eng},

number = {2},

pages = {103-109},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {A note on some discrete valuation rings of arithmetical functions},

url = {http://eudml.org/doc/248540},

volume = {036},

year = {2000},

}

TY - JOUR

AU - Schwab, Emil Daniel

AU - Silberberg, Gheorghe

TI - A note on some discrete valuation rings of arithmetical functions

JO - Archivum Mathematicum

PY - 2000

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 036

IS - 2

SP - 103

EP - 109

AB - 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.

LA - eng

KW - discrete valuation ring; arithmetical function; Dirichlet convolution; discrete valuation ring; arithmetical function; Dirichlet convolution

UR - http://eudml.org/doc/248540

ER -

## References

top- Karpilovsky G., Field theory, Marcel Dekker Inc. 1988, New York, Basel. (1988) Zbl0677.12010MR0972982
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- McCarthy P. J., Introduction to arithmetical functions, 1986, Springer-Verlag. Zbl0591.10003MR0815514
- Narkiewicz W., On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81–94. (1963) Zbl0114.26502MR0159778
- Schwab E. D., Multiplicative and additive elements in the ring of formal power series, PU.M.A. Vol. 4 (1993), 339–346. (1993) Zbl0806.13010MR1283983
- Yokom K. L., Totally multiplicative functions in regular convolution rings, Canadian Math. Bulletin 16 (1973), 119–128. (1973) MR0325502

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