Hilbert Nullstellensatz,” Theorem 10.34.1¶
The Stacks Project Authors. Hilbert Nullstellensatz,” Theorem 10.34.1.
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Domain-specific¶
- Maximal Ideal
- For a finitely generated algebra over an algebraically closed field \(k\), the weak Nullstellensatz identifies maximal ideals of \(k[x_1,\ldots,x_n]\) with point ideals \((x_1-a_1,\ldots,x_n-a_n)\).
This sourceEstablishes the maximal-ideal and residue-field facts for finite-type algebras over a field.
- For a finitely generated algebra over an algebraically closed field \(k\), the weak Nullstellensatz identifies maximal ideals of \(k[x_1,\ldots,x_n]\) with point ideals \((x_1-a_1,\ldots,x_n-a_n)\).
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