Properties of Ascending Chains for Partial Difference Polynomial Systems

Authors:
Gui-Lin Zhang;Xiao-Shan Gao
Affiliations:
Key Laboratory of Mathematics Mechanization Institute of Systems Science, AMSS, Chinese Academy of Sciences,;Key Laboratory of Mathematics Mechanization Institute of Systems Science, AMSS, Chinese Academy of Sciences,
Venue:
Computer Mathematics
Year:
2008

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Abstract

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.