Properties of Ascending Chains for Partial Difference Polynomial Systems

  • Gui-Lin Zhang
  • Xiao-Shan Gao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)


A characteristic set theory for partial difference polynomial systems is proposed. We introduce the concept of coherent and regular ascending chains and prove that a partial difference ascending chain is the characteristic set of its saturation ideal if and only if it is coherent and regular. This gives a method to decide whether a polynomial belongs to the saturation ideal of an ascending chain. We introduce the concept of strongly irreducible ascending chains and prove that a partial difference ascending chain is the characteristic set of a reflexive prime ideal if and only if it is strongly irreducible. This gives a simple and precise representation for reflexive prime ideals.


Ascending chain characteristic set coherent chain regular chain irreducible chain partial difference polynomial 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gui-Lin Zhang
    • 1
  • Xiao-Shan Gao
    • 1
  1. 1.Key Laboratory of Mathematics Mechanization Institute of Systems Science, AMSSChinese Academy of Sciences 

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