Examples
- Let R be an integral domain with K its field of fractions. Then every R-submodule of K is a fractional ideal. If R is Noetherian, every fractional ideal arises in this way.
- Finitely generated modules over the ring of integers Z coincide with the finitely generated abelian groups. These are completely classified by the structure theorem, taking Z as the principal ideal domain.
- Finitely generated modules over division rings are precisely finite dimensional vector spaces.
Read more about this topic: Finitely-generated Module
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