初等矩阵-Ore扩张的Quillen-Suslin定理的计算证明
Elementary matrix-computational proof of Quillen-Suslin theorem for Ore extensions
摘要：
本文给出了Ore扩张的Quillen-Suslin定理的一个初等矩阵构造性证明：若$K$是除环，$A:=K[x;σ,δ]$是Ore扩张，且有$σ$双射，则每一个可生成的投射$A$ -模是自由的.我们将展示一个算法，计算一个给定的投影生成的投射模的基础。该算法已在一个计算包中实现，并包括一些说明性的例子。
英文摘要：
In this short note we present an elementary matrix-constructive proof of Quillen-Suslin theorem for Ore extensions: If $K$ is a division ring and $A:=K[x;σ,δ]$ is an Ore extension, with $σ$ bijective, then every finitely generated projective $A$-module is free. We will show an algorithm that computes the basis of a given finitely generated projective module. The algorithm has been implemented in a computational package, and some illustrative examples are included.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
