Definition:Maximal Condition

Definition
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.

Also see

 * Definition:Ascending Chain Condition
 * Definition:Noetherian Module
 * Increasing Sequence in Ordered Set Terminates iff Maximal Element