\begin{definition}[Definition:Ascending Chain Condition/Module]
Let $R$ be a commutative ring with unity.
Let $M$ be an $R$-module.
Let $\struct {D, \subseteq}$ be a set of submodules of $M$ ordered by inclusion.
Then $M$ is said to have the '''ascending chain condition on submodules''' {{iff}}:
:''Every increasing sequence $N_1 \subseteq N_2 \subseteq N_3 \subseteq \cdots$ with $N_i \in D$ eventually stabilizes: $\exists k \in \N: \forall n \in \N, n \ge k: N_n = N_{n + 1}$''
\end{definition}