Geodesic
The valuated ring of the arithmetical functions as a power series ring
Archivum mathematicum, Tome 37 (2001) no. 1, pp. 77-80

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The paper examines the ring $A$ of arithmetical functions, identifying it to the domain of formal power series over ${\bf C}$ in a countable set of indeterminates. It is proven that $A$ is a complete ultrametric space and all its continuous endomorphisms are described. It is also proven that $A$ is a quasi-noetherian ring.
Classification : 13F25, 13F30
Keywords: arithmetical function; valuated ring; formal power series 
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     author = {Schwab, Emil D. and Silberberg, Gheorghe},
     title = {The valuated ring of the arithmetical functions as a power series ring},
     journal = {Archivum mathematicum},
     pages = {77--80},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2001},
     mrnumber = {1822767},
     zbl = {1090.13016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2001__37_1_a9/}
}
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Schwab, Emil D.; Silberberg, Gheorghe. The valuated ring of the arithmetical functions as a power series ring. Archivum mathematicum, Tome 37 (2001) no. 1, pp. 77-80. http://geodesic.mathdoc.fr/item/ARM_2001__37_1_a9/