# Rabinowitsch trick

From Encyclopedia of Mathematics

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].

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Rabinowitsch_trick&oldid=12019

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098