Hilbert's basis theorem
= Hilbert's basis theorem
{wiki=Hilbert's_basis_theorem}
Hilbert's Basis Theorem is a fundamental result in algebra, particularly in the theory of rings and ideals. It states that if \\( R \\) is a Noetherian ring (meaning that every ideal in \\( R \\) is finitely generated), then any ideal in the polynomial ring \\( R\[x\] \\) (the ring of polynomials in one variable \\( x \\) with coefficients in \\( R \\)) is also finitely generated.