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# Article

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Keywords:
arithmetical function; valuated ring; formal power series
Summary:
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.
References:
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[3] Schwab E.D., Silberberg G.: A Note on Some Discrete Valuation Rings of Arithmetical Functions. Arch. Math. (Brno), 36 (2000), 103–109. MR 1761615 | Zbl 1058.11007
[4] Sivaramakrishnan R.: Classical Theory of Arithmetic Functions. Monographs and Textbooks in Pure and Applied Mathematics 126, Marcel Dekker, 1989. MR 0980259 | Zbl 0657.10001
[5] Zariski O., Samuel P.: Commutative Algebra. vol. II, Springer Verlag, 1960. MR 0120249 | Zbl 0121.27801

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