On the Arithmetic of Strongly Primary Monoids

In this paper we study the arithmetic of strongly primary monoids. Numerical monoids and the multiplicative monoids of one-dimensional local Mori domains are main examples of strongly primary monoids. Our investigations focus on local tameness, a basic finiteness property in the theory of non-unique factorizations. It is well-known that locally tame strongly primary monoids have finite catenary degree and finite set of distances.