| Abstract | We construct an example of a finitely generated ideal I of R [ X ] , where R is a one-dimensional domain, whose leading terms ideal is not finitely generated. This gives a negative answer to the open question of whether if R is a domain with Krull dimension ≤1, then for any finitely generated ideal I of R [ X ] , the leading terms ideal of I is also finitely generated. Moreover, as a positive part of our answer, we prove that for any one-dimensional domain R and any a , b ∈ R , the ideal of R [ X ] generated by the leading terms of 〈 1 + a X , b 〉 is finitely generated. |
