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Pré-Publication, Document De Travail Année : 2018

A CHARACTERIZATION OF KRULL MONOIDS FOR WHICH SETS OF LENGTHS ARE (ALMOST) ARITHMETICAL PROGRESSIONS

Résumé

Let H be a Krull monoid with finite class group G and suppose that every class contains a prime divisor. Then sets of lengths in H have a well-defined structure which just depends on the class group G. With methods from additive combinatorics we establish a characterization of those class groups G guaranteeing that all sets of lengths are (almost) arithmetical progressions.
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Dates et versions

hal-01976941 , version 1 (10-01-2019)
hal-01976941 , version 2 (06-05-2019)

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Alfred Geroldinger, Wolfgang Schmid. A CHARACTERIZATION OF KRULL MONOIDS FOR WHICH SETS OF LENGTHS ARE (ALMOST) ARITHMETICAL PROGRESSIONS. 2018. ⟨hal-01976941v1⟩
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