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

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

2002-01-10

arxiv.org/abs/math/0201082v1

Archivum mathematicum 2004/2

Mathematics

Commutative Algebra

15 pages, no figures

Scientific paper

We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical functions with Dirichlet convolution and the power series ring on countably many variables. We topologize it with respect to a natural norm, and shove that all ideals are quasi-finite. Some elementary results on factorization into atoms are obtained. We prove the existence of an abundance of non-associate regular non-units.

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