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For a field $k$, by a "Nullstellensatz" over $k$, I mean an explicit description of the Galois connection between subsets of $k^n$ and ideals in the polynomial ring $k[x_1,\ldots,x_n]$. See this MO question of mine for more on this perspective.

Whenever one has a ring of functions on a space $X$, there is an induced Galois connection, hence one can ask for a Nullstellensatz: see page 15 of these notes for a(n unfortunately not yet very good) description of this perspective.

In particular there are analytic Nullstellensatze, for instance. I recently found this interesting note concerning the possibility of a Nullstellensatz for the ring of continuous functions on a compact space. (It shows that things work out nicely for maximal ideals and argues fairly convincingly that there is nothing good for all prime ideals. Somehow it did not completely extinguish my hopes, though.)

Certainly the term "Nullstellensatz" has been used for things which do not come under the aegis of the above. For instance, there is Alon's Combinatorial Nullstellensatz, which I unfortunately don't understand very well at all other than as some distant relative of the Chevalley-Warning theorem.

By the way, you say that most of the 200 papers are not referring (albeit obliquely) to Hilbert's Nullstellensatz? I find that somewhat hard to believe. Can you give some examples of far off uses of the term?

(Added: searching "anywhere" for Nullstellensatz on MathSciNet gives 632 matches. I should really turn in soon, so I can't look at them much now. I was surprised by how many of the most recent ones are referring to the Combinatorial Nullstellensatz, but apparently this is only 29 papers in all. By my very cursory glance, most of them do seem to be roughly in line with what I was suggesting above.)

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For a field $k$, by a "Nullstellensatz" over $k$, I mean an explicit description of the Galois connection between subsets of $k^n$ and ideals in the polynomial ring $k[x_1,\ldots,x_n]$. See this MO question of mine for more on this perspective.

Whenever one has a ring of functions on a space $X$, there is an induced Galois connection, hence one can ask for a Nullstellensatz: see page 15 of these notes for a(n unfortunately not yet very good) description of this perspective.

In particular there are analytic Nullstellensatze, for instance. I recently found this interesting note concerning the possibility of a Nullstellensatz for the ring of continuous functions on a compact space. (It shows that things work out nicely for maximal ideals and argues fairly convincingly that there is nothing good for all prime ideals. Somehow it did not completely extinguish my hopes, though.)

Certainly the term "Nullstellensatz" has been used for things which do not come under the aegis of the above. For instance, there is Alon's Combinatorial Nullstellensatz, which I unfortunately don't understand very well at all other than as some distant relative of the Chevalley-Warning theorem.

By the way, you say that most of the 200 papers are not referring (albeit obliquely) to Hilbert's Nullstellensatz? I find that somewhat hard to believe. Can you give some examples of far off uses of the term?