A note on certain semigroups of algebraic numbers

Maciej Radziejewski. "A note on certain semigroups of algebraic numbers." Colloquium Mathematicae 90.1 (2001): 51-58. <http://eudml.org/doc/283775>.

@article{MaciejRadziejewski2001,
abstract = {The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ 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.},
author = {Maciej Radziejewski},
journal = {Colloquium Mathematicae},
keywords = {Zaks-Skula function; Dirichlet series; Krull monoids; class groups},
language = {eng},
number = {1},
pages = {51-58},
title = {A note on certain semigroups of algebraic numbers},
url = {http://eudml.org/doc/283775},
volume = {90},
year = {2001},
}

TY - JOUR
AU - Maciej Radziejewski
TI - A note on certain semigroups of algebraic numbers
JO - Colloquium Mathematicae
PY - 2001
VL - 90
IS - 1
SP - 51
EP - 58
AB - The cross number κ(a) can be defined for any element a of a Krull monoid. The property κ(a) = 1 is important in the study of algebraic numbers with factorizations of distinct lengths. The arithmetic meaning of the weaker property, κ(a) ∈ 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.
LA - eng
KW - Zaks-Skula function; Dirichlet series; Krull monoids; class groups
UR - http://eudml.org/doc/283775
ER -