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Talk:Hadamard's lemma

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Nullstellensatz

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One direction to follow up on is possible ties to Hilbert's Nullstellensatz (weak version): a maximal ideal in the ring of polynomials in the variables (over an algebraically closed field) has the form . This yields a conclusion similar to Haramard's lemma as follows. Let be a polynomial and an arbitrary point. Since has a zero at , the ideal it generates cannot be the whole polynomial ring, and hence must be contained in some maximal ideal . This is equivalent to there being polynomials such that

identically for all ,

which is the same relation as in the Hadamard lemma. 130.239.235.159 (talk) 17:03, 5 November 2012 (UTC)[reply]