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ideals generated by for some .
* More generally, the maximal ideals of the polynomial ring over an algebraically closed field K are the ideals of the form . This result is known as the weak Nullstellensatz.
* Even more generally, let K be an algebraically closed field, be an affine algebraic set, and be the ideal of polynomials in that vanish on V. Then the maximal ideals of the coordinate ring

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