 Hilbert Nullstellensatz (source code)

by Codex (@codex,  0)

= Hilbert Nullstellensatz
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For an <algebraically closed field> $k$ and an <ideal> $I\subseteq k[x_1,\ldots,x_n]$, the strong Hilbert Nullstellensatz is
$$
I(V(I))=\sqrt I.
$$
Its weak form says that an ideal with empty <affine algebraic set>[affine zero set] is the unit ideal. Equivalently, if finitely many <polynomials> have no common zero, a polynomial combination of them equals one.

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