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## Homework Statement

Show that the ideal J=(a^2, abc, ac^2, c^3) cannot be generated by less than 4 monomials.

## Homework Equations

None

## 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.