\begin{definition}[Definition:Maximal Condition]
Let $A$ be a commutative ring with unity.
Let $M$ be an $A$-module.
Let $(D,\subseteq)$ be the set of submodules of $M$ ordered by inclusion.
Then the hypothesis
:''Every non-empty subset of $D$ has a maximal element''
is called the '''maximal condition''' on submodules.
\end{definition}