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arXiv · 1901.03506

A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions

Alfred Geroldinger·Wolfgang Schmid
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Abstract

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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Alfred Geroldinger, Wolfgang Schmid. 2019-01-11. A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions. https://arxiv.org/abs/1901.03506

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