ABSTRACT
Let H be a BF-monoid. By definition, H is half-factorial if and only if |L| = 1 for every L ∈ L(H) (equivalently, the set of distances ∆(H) is empty). If H is not halffactorial, then Proposition 1.2.10.3 shows that for every k ∈ N there is some a ∈ H such that |L(a)| ≥ k + 1. The principal purpose of this chapter is the description of the structure of large sets of lengths in arithmetically interesting cases.
