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On The Asymptotic Values of Length Functions In Krull And Finitely Generated commutative Monoids

Part of: Arithmetic rings and other special rings Semigroups Computational number theory

Published online by Cambridge University Press:  09 April 2009

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

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

MSC classification

Secondary: 20M14: Commutative semigroups 20M25: Semigroup rings, multiplicative semigroups of rings 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 11Y05: Factorization

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 3 , June 2003 , pp. 421 - 436
Copyright
Copyright © Australian Mathematical Society 2003

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