Definition:Minimal Condition

Definition
Let $A$ be a commutative ring with unity.

Let $M$ be an $A$-module.

Let $(D,\supseteq)$ be the set of submodules of $M$ ordered by "containation".

Then the hypothesis


 * Every non-empty subset of $D$ has a minimal element

is called the minimal condition on submodules.

Also see

 * Definition:Maximal Condition