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TitleOn the leading terms ideals of polynomial ideals over a valuation ring
Author(s) Samiha Monceur, Ihsen Yengui
TypeArticle in Journal
AbstractWe construct an example of a finitely generated ideal I of V [ X ] , where V is a one-dimensional valuation ring, whose leading terms ideal is not finitely generated. This gives a negative answer to the open question of whether if V is a valuation ring with Krull dimension ⩽1, then for any finitely generated ideal I of V [ X ] , the leading terms ideal of I is also finitely generated. The valuation rings satisfying this latter property will be called 1-Gröbner and are studied in this paper.
KeywordsGröbner bases, Gröbner rings, Gröbner ring conjecture, Valuation rings with zero-divisors, Krull dimension, Buchbergerʼs algorithm
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869311006715
LanguageEnglish
JournalJournal of Algebra
Volume351
Number1
Pages382 - 389
Year2012
Edition0
Translation No
Refereed No
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