Details:
Title  On the leading terms ideals of polynomial ideals over a valuation ring  Author(s)  Samiha Monceur, Ihsen Yengui  Type  Article in Journal  Abstract  We construct an example of a finitely generated ideal I of V [ X ] , where V is a onedimensional 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 1Gröbner and are studied in this paper.  Keywords  Gröbner bases, Gröbner rings, Gröbner ring conjecture, Valuation rings with zerodivisors, Krull dimension, Buchbergerʼs algorithm  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869311006715 
Language  English  Journal  Journal of Algebra  Volume  351  Number  1  Pages  382  389  Year  2012  Edition  0  Translation 
No  Refereed 
No 
