# Do Groebner bases give the smallest generating set for Ideals?

Given a Reduced Groebner Basis $(f_1,\ldots,f_n)$ for an ideal $I$, can there be another basis $(g_1,\ldots,g_m)$ for $I$ where $m<n$?

I've been reading through Cox, but can't seem to find an answer.

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Is the ideal $(x z - y^2, x^2 y - z^2, x^3 - y z)$ a counterexample? – Zhen Lin Apr 13 '13 at 16:24