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.
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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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