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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## 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.

#### Autorzy

• Maciej RadziejewskiFaculty of Mathematics and Computer Science