Factorization properties of Krull monoids with infinite class group

Wolfgang Hassler. "Factorization properties of Krull monoids with infinite class group." Colloquium Mathematicae 92.2 (2002): 229-242. <http://eudml.org/doc/285255>.

@article{WolfgangHassler2002,
abstract = {For a non-unit a of an atomic monoid H we call $L_H(a) = \{k ∈ ℕ | a = u₁... u_k with irreducible u_i ∈ H\}$ the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.},
author = {Wolfgang Hassler},
journal = {Colloquium Mathematicae},
keywords = {Krull monoids; Abelian groups; prime divisors; factorizations; groups of units; irreducible elements},
language = {eng},
number = {2},
pages = {229-242},
title = {Factorization properties of Krull monoids with infinite class group},
url = {http://eudml.org/doc/285255},
volume = {92},
year = {2002},
}

TY - JOUR
AU - Wolfgang Hassler
TI - Factorization properties of Krull monoids with infinite class group
JO - Colloquium Mathematicae
PY - 2002
VL - 92
IS - 2
SP - 229
EP - 242
AB - For a non-unit a of an atomic monoid H we call $L_H(a) = {k ∈ ℕ | a = u₁... u_k with irreducible u_i ∈ H}$ the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.
LA - eng
KW - Krull monoids; Abelian groups; prime divisors; factorizations; groups of units; irreducible elements
UR - http://eudml.org/doc/285255
ER -