Hilbert's basis theorem

Polynomial ideals are finitely generated

In mathematics, Hilbert's basis theorem asserts that every ideal of a polynomial ring over a field has a finite generating set (a finite basis in Hilbert's terminology). In modern algebra, rings whose ideals have this property are called Noetherian rings. Every field, and the ring of integers are Noetherian rings.

From Wikipedia, under CC BY-SA. More on occurri.