A ring in which every ascending chain of ideals stabilises (equivalently, every ideal is finitely generated). Hilbert basis theorem: k[x_1,…,x_n] is Noetherian. Backbone of commutative/algebraic-geometric finiteness.
A ring in which every ascending chain of ideals stabilises (equivalently, every ideal is finitely generated). Hilbert basis theorem: k[x_1,…,x_n] is Noetherian. Backbone of commutative/algebraic-geometric finiteness.