On The Asymptotic Values Of Length Functions In Krull And Finitely Generated Commutative Monoids

Let M be a commutative cancellative atomic monoid. We consider the behavior of the asymptotic length functions #(x) and L(x) on M . If M is finitely generated and reduced, then we present an algorithm for the computation of both #(x) and L(x) where x is a nonidentity element of M . We also explore the values that the functions #(x) and L(x) can attain when M is a Krull monoid with torsion divisor class group, and extend a well-known result of Zaks and Skula by showing how these values can be used to characterize when M is half-factorial