Geodesic
A note on certain semigroups of algebraic numbers
Maciej Radziejewski1
1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Matejki 48/49 60-769 Pozna/n, Poland
Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 51-58

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm90-1-4
Keywords: cross number kappa defined element krull monoid property kappa important study algebraic numbers factorizations distinct lengths arithmetic meaning weaker property kappa mathbb still unknown does define semigroup which may interesting its own right paper studies arithmetic divisor theory analytic distribution elements given norm properties semigroup related semigroup ideals

Maciej Radziejewski 1

1 Faculty of Mathematics and Computer Science Adam Mickiewicz University Matejki 48/49 60-769 Pozna/n, Poland 
@article{10_4064_cm90_1_4,
     author = {Maciej Radziejewski},
     title = {A note on certain semigroups of algebraic numbers},
     journal = {Colloquium Mathematicum},
     pages = {51--58},
     publisher = {mathdoc},
     volume = {90},
     number = {1},
     year = {2001},
     doi = {10.4064/cm90-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm90-1-4/}
}
TY  - JOUR
AU  - Maciej Radziejewski
TI  - A note on certain semigroups of algebraic numbers
JO  - Colloquium Mathematicum
PY  - 2001
SP  - 51
EP  - 58
VL  - 90
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm90-1-4/
DO  - 10.4064/cm90-1-4
LA  - en
ID  - 10_4064_cm90_1_4
ER  - 
%0 Journal Article
%A Maciej Radziejewski
%T A note on certain semigroups of algebraic numbers
%J Colloquium Mathematicum
%D 2001
%P 51-58
%V 90
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm90-1-4/
%R 10.4064/cm90-1-4
%G en
%F 10_4064_cm90_1_4
Maciej Radziejewski. A note on certain semigroups of algebraic numbers. Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 51-58. doi: 10.4064/cm90-1-4

Cité par Sources :