The set of minimal distances in Krull monoids

• Autorzy: Alfred Geroldinger , Qinghai Zhong
• Języki publikacji: EN

Abstrakty

EN

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 𝖫(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) ≤ max{exp(G)-2,𝗋(G)-1} and that equality holds if every class of G contains a prime divisor, which holds true for holomorphy rings in global fields.

Kategorie tematyczne

• 20M13: Arithmetic theory of monoids
• 13A05: Divisibility; factorizations
• 11B30: Arithmetic combinatorics; higher degree uniformity
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 2
• Strony: 97-120

Daty

wydano

2016

Twórcy

autor

Alfred Geroldinger

• Institute for Mathematics and Scientific Computing University of Graz, NAWI Graz, Heinrichstraße 36, 8010 Graz, Austria

autor

Qinghai Zhong

• Institute for Mathematics and Scientific Computing University of Graz, NAWI Graz, Heinrichstraße 36, 8010 Graz, Austria

Identyfikatory

DOI

10.4064/aa7906-1-2016