Sets of arithmetical invariants in transfer Krull monoids

Abstract

Abstract Transfer Krull monoids are a recently introduced class of monoids and include the multiplicative monoids of all commutative Krull domains as well as of wide classes of non-commutative Dedekind domains. We show that transfer Krull monoids are fully elastic (i.e., every rational number between 1 and the elasticity of the monoid can be realized as the elasticity of an element). In commutative Krull monoids which have sufficiently many prime divisors in all classes of their class group, the set of catenary degrees and the set of tame degrees are intervals. Without the assumption on the distribution of prime divisors, arbitrary finite sets can be realized as sets of catenary degrees and as sets of tame degrees.