As noted in math.stackexchange, the theorem is in part 3 of this paper: Hilbert, D. (1893). Über die vollen Invariantensysteme. Math. Ann. 42, pp. 313–373.

From a quick overview, I think the idea is to first prove the theorem when the set of common zeros is finite, using elimination theory. Edit: no, this is incorrect. Everything is done with homogeneous polynomials.

Now to find time to read it carefully.

As noted in math.stackexchange, the theorem is in part 3 of this paper: Hilbert, D. (1893). Über die vollen Invariantensysteme. Math. Ann. 42, pp. 313–373.

From a quick overview, I think the idea is to first prove the theorem when the set of common zeros is finite, using elimination theory. Everything is done with homogeneous polynomials.

Now to find time to read it carefully.

As noted in math.stackexchange, the theorem is in part 3 of this paper: Hilbert, D. (1893). Über die vollen Invariantensysteme. Math. Ann. 42, pp. 313–373.

From a quick overview, I think the idea is to first prove the theorem when the set of common zeros is finite, using elimination theory. Then he generalizes to infinite zero-sets. Everything is done with homogeneous polynomials.

Now to find time to read it carefully.

As noted in math.stackexchange, the theorem is in part 3 of this paper: Hilbert, D. (1893). Über die vollen Invariantensysteme. Math. Ann. 42, pp. 313–373.

From a quick overview, I think the idea is to first prove the theorem when the set of common zeros is finite, using elimination theory. Edit: no, this is incorrect. Everything is done with homogeneous polynomials.

Now to find time to read it carefully.