A note on certain semigroups of algebraic numbers
Tom 90 / 2001
Colloquium Mathematicum 90 (2001), 51-58
MSC: 11R27, 11N45, 11M41.
DOI: 10.4064/cm90-1-4
Streszczenie
The cross number $\kappa (a)$ can be defined for any element $a$ of a Krull monoid. The property $\kappa (a) = 1$ is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, $\kappa (a) \in {\mathbb Z}$, is still unknown, but it does define a semigroup which may be interesting in its own right. This paper studies some arithmetic (divisor theory) and analytic (distribution of elements with a given norm) properties of that semigroup and a related semigroup of ideals.
