A counterexample to the Gröbner ring conjecture.

We propose a counterexample to the Gröbner ring conjecture in the irrational case. More precisely, we construct a valuation domain V of Krull dimension 1 and a finitely generated ideal J of V [ X , Y ] equipped with some irrational monomial order <, such that the ideal LT < (J) generated by the leading terms of the elements of J is not finitely generated. [ABSTRACT FROM AUTHOR]