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

2019/01/11 by Geroldinger, Alfred, Schmid, Wolfgang
#Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.03506

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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