Difference indices of quasi-prime difference algebraic systems. (July 2018) - Wang, Jie
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 for difference indices is given. As applications, an upper bound for the Hilbert–Levin regularity and an effective difference ideal membership theorem for quasi-prime difference algebraic systems are deduced.