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

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.

arXiv commentTo appear in Rev. Mat. Iberoamericana. The content of this preprint was initially disseminated as part (mostly Chapter 4) of an early version of the manuscript ''A characterization of class groups via sets of lengths'' (hal-01131955, version 1 and arXiv:1503.04679v1) by the same authors