拟素差代数系统的差指数
Difference Index of Quasi-Prime Difference Algebraic Systems
摘要：
本文主要研究拟素差分代数系统的差分指标。定义了拟素差分代数系统的拟维数多项式。在此基础上，通过一族伪雅可比矩阵给出了拟素差分代数系统的差分指标的定义。证明了差分指标的一些性质。特别地，给出了差分指标的一个上界.作为应用，给出了Hilbert-Levin正则性的一个上界和差分理想隶属度问题的一个阶数上界.
英文摘要：
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.
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