An Algorithmic Proof of Suslin′s Stability Theorem for Polynomial Rings
An Algorithmic Proof of Suslin′s Stability Theorem for Polynomial Rings
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DOI：
10.1006/jabr.1995.1349
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发表时间：
1994-05
影响因子：
0.9
通讯作者：
Hyungju Park;C. Woodburn
中科院分区：
文献类型：
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作者：
Hyungju Park;C. Woodburn
设k是一个域。然后，k上的高斯消去法和一元多项式环k[x]的欧氏除法算法允许我们将SLn（k）或SLn（k[x]）中的任何矩阵，n ≥ 2，写为初等矩阵的乘积。Suslin的稳定性定理指出，对于SLn（k[xl，…，xm]），其中n ≥ 3且m ≥ 1。本文给出了Suslin稳定性定理的算法证明，从而提供了一种求给定多项式矩阵到初等矩阵的显式因式分解的方法。在算法的实现中可以使用Grobner基技术。
Abstract Let k be a field. Then Gaussian elimination over k and the Euclidean division algorithm for the univariate polynomial ring k[x] allow us to write any matrix in SLn(k) or SLn(k[x]), n ≥ 2, as a product of elementary matrices. Suslin′s stability theorem states that the same is true for SLn(k[xl,..., xm]) with n ≥ 3 and m ≥ 1. In this paper, we present an algorithmic proof of Suslin′s stability theorem, thus providing a method for finding an explicit factorization of a given polynomial matrix into elementary matrices. Grobner basis techniques may be used in the implementation of the algorithm.