Abstract
The set of distances of a monoid or of a domain is the set of all d∈N with the following property: there are irreducible elements u1,…,uk,v1,…,vk+d such that u1⋅…⋅uk=v1⋅…⋅vk+d, but u1⋅…⋅uk cannot be written as a product of l irreducible elements for any l with k<l<k+d. We show that the set of distances is an interval for certain seminormal weakly Krull monoids which include seminormal orders in holomorphy rings of global fields.
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