The set of minimal distances in Krull monoids

Alfred Geroldinger, and Qinghai Zhong. "The set of minimal distances in Krull monoids." Acta Arithmetica 173.2 (2016): 97-120. <http://eudml.org/doc/279155>.

@article{AlfredGeroldinger2016,
abstract = {Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say $a= u_1 · ... · u_k$. The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every class of G contains a prime divisor, which holds true for holomorphy rings in global fields.},
author = {Alfred Geroldinger, Qinghai Zhong},
journal = {Acta Arithmetica},
keywords = {nonunique factorizations; sets of distances; Krull monoids; zerosum sequences; cross numbers},
language = {eng},
number = {2},
pages = {97-120},
title = {The set of minimal distances in Krull monoids},
url = {http://eudml.org/doc/279155},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Alfred Geroldinger
AU - Qinghai Zhong
TI - The set of minimal distances in Krull monoids
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 2
SP - 97
EP - 120
AB - Let H be a Krull monoid with class group G. Then every nonunit a ∈ H can be written as a finite product of atoms, say $a= u_1 · ... · u_k$. The set (a) of all possible factorization lengths k is called the set of lengths of a. If G is finite, then there is a constant M ∈ ℕ such that all sets of lengths are almost arithmetical multiprogressions with bound M and with difference d ∈ Δ*(H), where Δ*(H) denotes the set of minimal distances of H. We show that max Δ*(H) ≤ maxexp(G)-2,(G)-1 and that equality holds if every class of G contains a prime divisor, which holds true for holomorphy rings in global fields.
LA - eng
KW - nonunique factorizations; sets of distances; Krull monoids; zerosum sequences; cross numbers
UR - http://eudml.org/doc/279155
ER -