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• # Artykuł - szczegóły

## Acta Arithmetica

2016 | 173 | 2 | 97-120

## The set of minimal distances in Krull monoids

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.

97-120

wydano
2016

### Twórcy

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