2002/01/10 by Jan Snellman
Mathematics · #math.AC #msc:11A25 #msc:13J05
published as Archivum mathematicum 2004/2 · 15 pages, no figures
arxiv created 2002/01/10 · arxiv updated 2009/11/30
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.