ABSTRACT
By an arithmetical function f, we mean a map f : ℕ → ℂ, where ℕ denotes the set of positive integers and ℂ stands for the set of complex numbers. The ring https://www.w3.org/1998/Math/MathML"> A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351023344/b6c68d68-1226-4347-aaa8-58dfe0c0d0a9/content/eq621.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> of arithmetical functions (under addition and Dirichlet composition) is shown to be a UFD by an isomorphism with ℂ ω , the ring of formal powers series in countably infinite indeterminates. This elegant theorem is due to E. D. Cashwell and C. J. Everett (1959) [ 3 ].
