This post is about examples of some nice things that could fail for modules that are not finitely generated (or not finitely presented when the ring is not Noetherian).
1. Nakayama’s Lemma (Krull’s Intersection Theorem)
2.
.
3.
for
a flat
-module
4. 
5. Finitely Generated Nil Ideal is Nilpotent
6. Finitely presented flat module is projective




