Hilbert Revisited
نویسنده
چکیده
Hilbert was concerned with fundamental problems of invariant theory: given a linear group, G, acting linearly on the ring of polynomials, S = K[X1, . . . , XN ], we let S be the subring of invariants. Is S nitely generated as an algebra over the eld, K, and if so, what are its generators? Assuming it is nitely generated, that is, that S = K[Y1, . . . , YN ′ ]/I, is it the case that I is nitely generated as an ideal in K[Y1, . . . , YN ′ ]? (The ideal, I, is called the ideal of relations on the invariants.) To answer the latter question, Hilbert proved his famous Basis Theorem, undeniably one of the cornerstones of commutative algebra.
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