The Rabinowitsch trick is a technique used in number theory, particularly in the field of algebraic number theory and in the study of polynomial divisibility. It is named after the mathematician Solomon Rabinowitsch. The trick primarily involves the manipulation of polynomials to demonstrate certain divisibility properties. Specifically, it is often applied in the context of proving that a polynomial is divisible by another polynomial under certain conditions.
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To prove the Strong Hilbert Nullstellensatz from its weak form, adjoin a variable and the equation . If vanishes on , the ideal has no common zero and is therefore the unit ideal. Substituting and clearing denominators yields for some .