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

Abstract

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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.

How to cite

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Schwab, 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

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  1. Karpilovsky G., Field theory, Marcel Dekker Inc. 1988, New York, Basel. (1988) Zbl0677.12010MR0972982
  2. McCarthy P. J., Regular arithmetical convolutions, Portugal. Math. 27 (1968), 1–13. (1968) Zbl0203.35304MR0271015
  3. McCarthy P. J., Introduction to arithmetical functions, 1986, Springer-Verlag. Zbl0591.10003MR0815514
  4. Narkiewicz W., On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81–94. (1963) Zbl0114.26502MR0159778
  5. 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
  6. Yokom K. L., Totally multiplicative functions in regular convolution rings, Canadian Math. Bulletin 16 (1973), 119–128. (1973) MR0325502

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