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July 5

prove that not Grobner base

Let S = K[r,s,t,u,v,w,x,y} and I the ideal of S generated by f = sy-ux , g = rw-tv , h = rt-su ,Show that there exist no monomial order < o S such that {f,g,h } I a Grobner basis of I with respect to < .

— Preceding unsigned comment added by 182.187.77.255 (talk • contribs) 04:56, 5 July 2013‎

If you want some hints, you should present the context more clearly.

I suppose that you intend K to be a field, and K[r,s,t,u,v,w,x,y} [SIC!] the commutative polynomial ring over that field. Is that correct?

In what kind of coursis or other context did you get the question? Specifically, have you access to tools to decide whether or not S is a Koszul algebra? (Note, that if the "denominator" ideal for a homogeneous ring of this type has a Gröbner basis with only quadratic (homogeneous) elements, then it is necessarily Koszul.) JoergenB (talk) 21:39, 5 July 2013 (UTC)[reply]