Dynamical Grobner bases

JOURNAL OF ALGEBRA

卷:301

Article

Yengui, Ihsen

关键词: dynamical Grobner basis;    ideal membership problem;    valuation rings;    Noetherian rings;    principal rings;   

DOI  :  10.1016/j.jalgebra.2006.01.051

来源: Elsevier

【 摘 要 】

In this paper, we introduce the notion of dynamical Grobner bases of polynomial ideals over a principal ring. As application, we solve dynamically a fundamental algorithmic question in the theory of multivariate polynomials over the integers called Kronecker's problem, that is the problem of finding a decision procedure for the ideal membership problem for Z[X-1,..., X-n]. The notions of Grobner bases over Noetherian valuation rings and dynamical Grobner bases over principal rings have applications in error correcting codes. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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