A ring \(R\) is Noetherian if it satisfies the ascending chain condition on ideals: for every chain of ideals \(I_1 \subseteq I_2 \subseteq \cdots\) of \(R\) there exists \(N\geq 1\) such that \(I_N = I_{N+1} = \cdots\). Guide AppearancesCommutative algebraWhat links to thisCommutative algebraDomains and factorizationPolynomial rings