Density of direct factors in normed arithmetical semi-groups.

Abstract

In 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.