On products of k atoms - Gao, Weidong; Geroldinger, Alfred (Monatshefte für Mathematik, 2009)
. Let H be an atomic monoid. For let denote the set of all with the following property: There exist atoms (irreducible elements) u 1 , …, u k , v 1 , …, v m ∈ H with u 1 · … · u k = v 1 · … · v m . We show that for a large class of noetherian domains satisfying some natural finiteness conditions, the sets are almost arithmetical progressions. Suppose that H is a Krull monoid with finite cyclic class group G such that every class contains a prime (this includes the multiplicative monoids of rings of integers of algebraic number fields). We show that, for every , max which settles Problem 38 in [4].