A pure power product version of the Hilbert Nullstellensatz.
W. Dale Brownawell · The Michigan Mathematical Journal · 1998
BackgroundLet k be a field and R = k[x 0 , . .., x n ].Then what one might call the radical version of Hilbert's Nullstellensatz states that, for any homogeneous ideal A = (f 1 , . .., f m ) with radical R, some power of R lies in A: R e ⊂ A.From now on, let us denote by e the minimum such exponent for this A.Rabinowitsch [Ra] showed that this formulation is equivalent to the following (apparently weaker) assertion, which has been called the Bezout version of the Nullstellensatz: If g 1 , . .., g m in S = k[x 1 , . .., x n ] have no common zeros (say, in an algebraic closure of k), then there exist a 1 , . ..,