Hilbert Nullstellensatz吗

Arch. Formal Proofs Pub Date : 1900-01-01 DOI:10.1017/9781316683002.039

Alexander Maletzky

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引用次数: 5

摘要

设k是一个代数闭域。我们将使用以下符号。如果I∧k[X1，…]， Xn]是一个理想，我们设Z(I)表示an中的仿射代数集，该仿射代数集由I中的多项式消失所定义。相反，如果X是仿射代数集，则I(X)表示k[X1，…]中多项式的理想。， Xn]在X上消失。我们将给出以下结果的证明，称为弱Nullstellensatz:

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Hilbert's Nullstellensatz

Let k be an algebraically closed field. We will employ the following notation. If I ⊂ k[X1, . . . , Xn] is an ideal, we let Z(I) denote the affine algebraic set in An defined by the vanishing of the polynomials in I . Conversely, if X is an affine algebraic set, I(X) denotes the ideal of polynomials in k[X1, . . . , Xn] vanishing on X . We will give a proof of the following result, called the weak Nullstellensatz:

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Arch. Formal Proofs

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