1. The problem statement, all variables and given/known data Show that the ideal J=(a^2, abc, ac^2, c^3) cannot be generated by less than 4 monomials. 2. Relevant equations None 3. The attempt at a solution I was thinking of computer a Groebner basis for this (which is what I ended up doing) However, I'm not sure how I can show there it cannot be generated by less than 4 monomials. I do know that this ideal is indeed also a Groebner basis, but not sure where to go from here.