Differential Nullstellensatz
The differential Nullstellensatz is the analogue in differential algebra of Hilbert's nullstellensatz.
- A differential ideal or ∂-ideal is an ideal closed under ∂.
- An ideal is called radical if it contains all roots of its elements.
Suppose that K is a differentially closed field of characteristic 0. . Then Seidenberg's differential nullstellensatz states there is a bijection between
- Radical differential ideals in the ring of differential polynomials in n variables, and
- ∂-closed subsets of Kn.
This correspondence maps a ∂-closed subset to the ideal of elements vanishing on it, and maps an ideal to its set of zeros.
Read more about this topic: Differentially Closed Field
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