J. Aust. Math. Soc.  74 (2003), 421-436
On the asymptotic values of length functions in Krull and finitely generated commutative monoids

S. T. Chapman
  Trinity University
  Department of Mathematics
  715 Stadium Drive
  San Antonio, Texas 78212-7200
  USA
  schapman@trinity.edu
and
J. C. Rosales
  Departamento de Álgebra
  Universidad de Granada
  E-18071 Granada
  Spain
  jrosales@ugr.es


Abstract
Let  M be a commutative cancellative atomic monoid. We consider the behaviour of the asymptotic length functions $\bar{\ell} (x)$ and $\bar{L}(x)$ on  M. If  M is finitely generated and reduced, then we present an algorithm for the computation of both $\bar{\ell} (x)$ and $\bar{L} (x)$ where $x$ is a nonidentity element of  M. We also explore the values that the functions $\bar{\ell} (x)$ and $\bar{L} (x)$ 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.
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