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##
The Groebner Ring Conjecture in One Variable

fichier pdf.

with Peter Schuster and Ihsen Yengui.

To appear in Math. Zeitschrift.

** Abstract **

We prove that a valuation
domain **V** has Krull dimension ≤
1 if and only if for every
finitely generated ideal *J* of **V**[X] the ideal generated by the leading terms of elements of *J* is also
finitely generated. This proves the Groebner ring
conjecture in one variable.
The proof we give is both simple and constructive.
The same result is valid for semihereditary rings.