Viewing topic: Hilbert's Nullstellensatz

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Hilbert's Nullstellensatz

  • Definition: The maximal ideals of the polynomial ring C[x_1,...,x_n] are in bijective correspondence with points of complex n-dimensional space. A point a=(a_1,...,a_n) of C^n corresponds to the kernel M_a of the substitution map s_a:C[x_1,...,x_n] -> C that sends x_i to a_i. The kernel M_a is generated by the n linear polynomials x_i - a_i.

    Source: Algebra, second edition by Michael Artin

  • Example: The German word Nullstellensatz is a combination of three words whose translations are zero, places, theorem.

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