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,}|
Rabinowitsch trick. W. Dale Brownawell (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Rabinowitsch_trick&oldid=12019