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. Gordan (1868)
proved the existence of finite fundamental systems of algebraic invariants and covariants
for any binary quadratic form, which in modern
terminology would be stated that every binary quadratic form has a finite Hilbert
basis. The complete systems of the quintic and sextic were also first obtained
by Gordan in 1868.
Hilbert (1890) subsequently proved the general Hilbert
basis theorem, which is a finiteness theorem for the related concept of syzygies.
Gordan, P. "Beweis, dass jede Covariante und Invariante einer binären Form eine ganze Funktion mit numerischen Coeffizienten einer endlichen
Anzahl solcher Formen ist." J. reine angew. Math.69, 323-354,
1868.Hilbert, D. "Über die Theorie der algebraischen Formen."
Math. Ann.36, 473-534, 1890.
