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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-1-4,
author = {Maciej Radziejewski},
title = {A note on certain semigroups of algebraic numbers},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {51-58},
zbl = {0998.11056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-1-4}
}
Maciej Radziejewski. A note on certain semigroups of algebraic numbers. Colloquium Mathematicae, Tome 89 (2001) pp. 51-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-1-4/