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STRUCTURE OF GRÖBNER BASES WITH RESPECT TO ELIMINATION ORDERS

In this paper we study the structure of Gröbner bases with respect to elimination orders. We give a structure theorem for such Gröbner bases, which turns out to be an extension of Lazard’s theorem established in the case of two variables. We then give a more precise structure theorem in the case of radical zerodimensional ideals. As an application of this we give the basic theoretical ingredients of an algorithm to compute a lexicographic Gröbner basis of a finite intersection of maximal ideals.