诺特赋值环上Gr(o)bner基的性质

摘要

本文主要研究了诺特赋值环上多项式理想的Gr(o)bner基的性质.利用Buchberger算法,证明了约化Gr(o)bner基的存在性及当其首项系数为单位元时的唯一性.推广了极小Gr(o)bner基和约化Gr(o)bner基的概念.同时,我们给出了求极小Gr(o)bner基和约化Gr(o)bner基的算法.%In this paper, we consider the properties of Grobner basis of polynomial ideal over a noetherian valuation ring. By using Buchberger's algorithm, we prove the existence of reduced Grobner basis and the uniqueness when the leading coefficient is a inverse, which extend the concept of minimal and reduced Grobner basis. Meanwhile, we provide a algorithm to compute minimal and reduced Grobner basis.