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Let be a Krull monoid with finite class group and suppose that every class contains a prime divisor. Then sets of lengths in have a well-defined structure which depends only on the class group . With methods from additive combinatorics we establish a characterization of those class groups guaranteeing that all sets of lengths are (almost) arithmetical progressions.
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Alfred Geroldinger, Wolfgang Alexander Schmid, A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions. Rev. Mat. Iberoam. 37 (2021), no. 1, pp. 293–316DOI 10.4171/RMI/1207