Rabinowitsch trick

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This "trick" deduces the general Hilbert Nullstellensatz (cf. Hilbert theorem) from the special case that the polynomials have no common zeros. Indeed, let , where is a field. If vanishes on the common zeros of , then there are polynomials such that

Substitution of into this identity and clearing out the denominator shows that

where and . This ingenious device was published in the one(!) page article [a1].


[a1] J.L. Rabinowitsch, "Zum Hilbertschen Nullstellensatz" Math. Ann. , 102 (1929) pp. 520,}
How to Cite This Entry:
Rabinowitsch trick. W. Dale Brownawell (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098