Context:
Let $R$ be a local ring and $M$ an $R$-module. Show that the set of all submodules of $M$ is totally ordered by inclusion iff every finitely generated submodule of $M$ is cyclic or, equivalently, iff every $2$-generator submodule is cyclic.
2026-05-13 17:27:04.1778693224
What's a $2$-generator submodule?
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A submodule that is generated by two elements. (This isn't exactly a standard or well-known term, but in that context there's nothing else it could sensibly mean.)