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TitleGröbner Bases in Orders of Algebraic Number Fields
Author(s) David Andrew Smith
TypeArticle in Journal
AbstractWe prove that any orderOof any algebraic number field K is a reduction ring. Rather than showing the axioms for a reduction ring hold, we start from scratch by well-orderingO, defining a division algorithm, and demonstrating how to use it in a Buchberger algorithm which computes a Gröbner basis given a finite generating set for an ideal. It is shown that our theory of Gröbner bases is equivalent to the ideal membership problem and in fact, a total of eight characterizations are given for a Gröbner basis. Additional conclusions and questions for further investigation are revealed at the end of the paper.
Length12
File
URL dx.doi.org/10.1006/jsco.2001.0501
LanguageEnglish
JournalJournal of Symbolic Computation
Volume33
Number2
Pages209-220
Year2002
MonthFebruary
Translation No
Refereed No
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