# A note on certain semigroups of algebraic numbers

Colloquium Mathematicae (2001)

- Volume: 90, Issue: 1, page 51-58
- ISSN: 0010-1354

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topMaciej 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 -

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