Geodesic
A note on some discrete valuation rings of arithmetical functions
Archivum mathematicum, Tome 36 (2000) no. 2, pp. 103-109.

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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.
Classification : 11A25, 13F30
Keywords: discrete valuation ring; arithmetical function; Dirichlet convolution 
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     author = {Schwab, Emil D. and Silberberg, Gheorghe},
     title = {A note on some discrete valuation rings of arithmetical functions},
     journal = {Archivum mathematicum},
     pages = {103--109},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2000},
     mrnumber = {1761615},
     zbl = {1058.11007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000__36_2_a2/}
}
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Schwab, Emil D.; Silberberg, Gheorghe. A note on some discrete valuation rings of arithmetical functions. Archivum mathematicum, Tome 36 (2000) no. 2, pp. 103-109. http://geodesic.mathdoc.fr/item/ARM_2000__36_2_a2/