# Definition:Minimal Condition/Submodule Ordering

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## Definition

Let $A$ be a commutative ring with unity.

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

Let $\struct {D, \supseteq}$ be the set of submodules of $M$ ordered by the subset relation.

This article, or a section of it, needs explaining.Is there a good reason why the relation is reversed? This is at odds with how the subset relation is implemented in general.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |

Then the hypothesis:

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

is called the **minimal condition** on submodules.

## Also see

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