Difference Index of Quasi-Prime Difference Algebraic Systems

2016/07/16 by Jie Wang, Wang, Jie
Mathematics · #12H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:12H10

paper · pdf · doi:10.48550/arxiv.1607.04732

14 pages. arXiv admin note: substantial text overlap with arXiv:1607.04076

arxiv created 2016/07/16 · arxiv updated 2016/07/19

Abstract

This paper is devoted to studying difference indices of quasi-prime difference algebraic systems. We define the quasi dimension polynomial of a quasi-prime difference algebraic system. Based on this, we give the definition of the difference index of a quasi-prime difference algebraic system through a family of pseudo-Jacobian matrices. Some properties of difference indices are proved. In particular, an upper bound of difference indices is given. As applications, an upper bound of the Hilbert-Levin regularity and an upper bound of orders for difference ideal membership problem are deduced.

Citations

• Difference Index of Quasi-regular Difference Algebraic Systems

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