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Valuation Extensions of Algebras Defined by Monic Gröbner Bases

✍ Scribed by Huishi Li

Book ID
118794840
Publisher
Springer Netherlands
Year
2011
Tongue
English
Weight
392 KB
Volume
15
Category
Article
ISSN
1386-923X

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✍ David Andrew Smith 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 281 KB

We prove that any order O of 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-ordering O, defining a division algorithm, and demonstrating how to use it in a Buchberger algorithm which computes a Gröbner basis g