Displaying similar documents to “A note on some discrete valuation rings of arithmetical functions”

The ring of arithmetical functions with unitary convolution: Divisorial and topological properties

Jan Snellman (2004)

Archivum Mathematicum

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We study ( 𝒜 , + , ) , the ring of arithmetical functions with unitary convolution, giving an isomorphism between ( 𝒜 , + , ) and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] between the ring ( 𝒜 , + , · ) of arithmetical functions with Dirichlet convolution and the power series ring [ [ x 1 , x 2 , x 3 , ] ] on countably many variables. We topologize it with respect to a natural norm, and show that all ideals are quasi-finite. Some elementary results on factorization...