Analogs of Gröbner Bases in Polynomial Rings over a Ring
Analogs of Gröbner Bases in Polynomial Rings over a Ring
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环上多项式环中 Gröbner 基的类比
DOI：
10.1006/jsco.1996.0006
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Lyn J. Miller
中科院分区：
文献类型：
--
作者：
Lyn J. Miller
本文定义了多项式环R [x1，...，...]中R -子代数及其理想的Grobner基的类似，xn]其中R是一个具有乘法单位元的Noether整环，在这个整环中我们可以确定理想隶属度和计算合合模.主要目的是提出和验证构造这些Grobner基对应物的算法.作为应用，我们将给出一个计算R [x1，...，其中每个合点的每个坐标必须是子代数的元素。
Abstract In this paper we will define analogs of Grobner bases for R -subalgebras and their ideals in a polynomial ring R [ x 1 ,..., x n ] where R is a noetherian integral domain with multiplicative identity and in which we can determine ideal membership and compute syzygies.The main goal is to present and verify algorithms for constructing these Grobner basis counterparts.As an application, we will produce a method for computing generators for the first syzygy module of a subset of an R [ x 1 ,..., x n ] where each coordinate of each syzygy must be an element of the subalgebra.