  Let $R$ be a commutative ring. A full additive subcategory $\C$ of
$R$-modules is triangulated if whenever two terms of a short exact sequence
belong to $\C$, then so does the third term. In this note we give a
classification of triangulated subcategories of finitely generated modules over
a principal ideal domain. As a corollary we show that in the category of
finitely generated modules over a PID, thick subcategories (triangulated
subcategories closed under direct summands), wide subcategories (abelian
subcategories closed under extensions) and Serre subcategories (wide
subcategories closed under kernels) coincide and correspond to specialisation
closed subsets of $\Spec(R)$.
