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 . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa7906-1-2016,
author = {Alfred Geroldinger and Qinghai Zhong},
title = {The set of minimal distances in Krull monoids},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {97-120},
zbl = {06586876},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa7906-1-2016}
}
Alfred Geroldinger; Qinghai Zhong. The set of minimal distances in Krull monoids. Acta Arithmetica, Tome 172 (2016) pp. 97-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa7906-1-2016/