THE VALUATED RING OF THE ARITHMETICAL FUNCTIONS AS A POWER SERIES RING

Emil D. Schwab and Gheorghe Silberberg

Address. Emil D. Schwab, Department of Mathematics, University of Oradea, str. Armatei Romane nr. 5, 3700 Oradea, ROMANIA
               and
               Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, 79968-0514, USA

               Gheorghe Silberberg, Department of Economics, Central European University, Nador u. 9, 1051 Budapest, HUNGARY

E-mail:   CPHSIG01@phd.ceu.hu

Abstract. 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.

AMSclassification. 13F25, 13F30

Keywords. Arithmetical function, valuated ring, formal power series.