The valuated ring of the arithmetical functions as a power series ring

Abstract

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.