Terminating Euclidean algorithm for a non-Noetherian Bézout domain

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• 作者：Hyukmin Kwon ^{khm@postech.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11A05 ; 13F07 ; 20Gxx ; 08B25
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：506
• 期：Complete
• 页码：10-32
• 全文大小：329 K

文摘

In this paper, we will define a Euclidean-like norm and a division algorithm for a non-Noetherian Bézout domain, k[y]+x⋅k(y)[x]$k[y]+x\cdot k(y)[x]$, where k   is a field. And we will show that the Euclidean algorithm for that domain always terminates. As its application, we will give an algorithm to find the normal form of any matrix in GL₂(k[x,y])$G{L}_2(k[x,y])$ over k, with respect to the amalgamated free product structure.