= Solution
The <structure theorem for finitely generated modules over a principal ideal domain> applies because a <Euclidean domain> is a <principal ideal domain>. For a finitely generated $R$-<module>,
$$
\boxed{M\cong R^r\oplus R/(d_1)\oplus\cdots\oplus R/(d_s),\qquad d_1\mid d_2\mid\cdots\mid d_s,}
$$
where the $d_i$ are nonzero nonunits. The free rank $r$ and the <invariant factors of a finitely generated module> $d_i$ are unique, with each $d_i$ determined up to multiplication by a unit. Equivalently, the <torsion submodule> decomposes into cyclic <modules> $R/(P^a)$ for irreducible $P$, with uniquely determined prime-power elementary factors.
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