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.
@article{107723,
author = {Emil Daniel Schwab and Gheorghe Silberberg},
title = {A note on some discrete valuation rings of arithmetical functions},
journal = {Archivum Mathematicum},
volume = {036},
year = {2000},
pages = {103-109},
zbl = {1058.11007},
mrnumber = {1761615},
language = {en},
url = {http://dml.mathdoc.fr/item/107723}
}
Schwab, Emil Daniel; Silberberg, Gheorghe. A note on some discrete valuation rings of arithmetical functions. Archivum Mathematicum, Tome 036 (2000) pp. 103-109. http://gdmltest.u-ga.fr/item/107723/
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