I'm looking for an example of a finitely generated module with submodules that are not finitely generated.
I've found a similar question dealing with group (i.e. an example of a finitely generated group with subgroups that are not finitely generated). But I can't figure out whether that question do help to this one.
And I actually want to find a more "module-like" example rather than an example derived from a 'strange' group.
Can you please help? Thank you!