The ring of arithmetical functions with unitary convolution: Divisorial and topological properties
We study , the ring of arithmetical functions with unitary convolution, giving an isomorphism between and a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett [NumThe] 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 show that all ideals are quasi-finite. Some elementary results on factorization into atoms...