Difference Index of Quasi-Prime Difference Algebraic Systems
Commutative Algebra
2016-07-19 v1
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.
Keywords
Cite
@article{arxiv.1607.04732,
title = {Difference Index of Quasi-Prime Difference Algebraic Systems},
author = {Jie Wang},
journal= {arXiv preprint arXiv:1607.04732},
year = {2016}
}
Comments
14 pages. arXiv admin note: substantial text overlap with arXiv:1607.04076