Let $R$ be a ring and let $M$ be an $R$-module. Then $M$ is Noetherian (or satisfies the ascending chain condition on submodules) if there are no infinite increasing chains of submodules. That is, if whenever $M_1\subseteq M_2\subseteq M_3\subseteq \cdots$ is an increasing chain of submodules of $M$, then there is a positive integer $m$ such that for all $k\geq m$, $M_k=M_m$.
Wikidata ID: Q2444982