Thomas, John R.2009-04-172009-04-1719771977Source: Masters Abstracts International, Volume: 45-06, page: 3174.http://hdl.handle.net/10393/10701http://dx.doi.org/10.20381/ruor-16959In this thesis we study direct factors A and B of normed arithmetical semi-groups. Essentially, we prove that such direct factors have asymptotic densities. The generality of this result is restricted to unique factorization semi-groups whose counting functions satisfy some regularity conditions. The treatment is broad enough, however, to include, in addition to the semi-group N* of positive integers, analogous "normalized" semi-groups of Gaussian integers and other algebraic integers.77 p.Mathematics.Thesis