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A set of Algebraic Invariants for a Quantic such that any invariant of the Quantic
is expressible as a Polynomial in members of the set. In 1868, Gordan proved the existence of finite fundamental systems
of algebraic invariants and covariants for any binary Quantic. In 1890, Hilbert 
(1890) proved the
Hilbert Basis Theorem, which is a finiteness theorem for the related concept of Syzygies.
See also Hilbert Basis Theorem, Syzygy
References
Hilbert, D. ``Über die Theorie der algebraischen Formen.'' Math. Ann. 36, 473-534, 1890.