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Article

Schwab, Emil D. ; Silberberg, Gheorghe
A note on some discrete valuation rings of arithmetical functions. (English). Archivum Mathematicum, vol. 36 (2000), issue 2, pp. 103-109
MSC: 11A25, 13F30 | MR 1761615 | Zbl 1058.11007
Keywords:
discrete valuation ring; arithmetical function; Dirichlet convolution
Summary:
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.
References:
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[6] Yokom K. L.: Totally multiplicative functions in regular convolution rings. Canadian Math. Bulletin 16 (1973), 119–128. MR 0325502
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