= Invariant factor of a finitely generated module
{title2=$d_1\mid\cdots\mid d_k$}
= Invariant factors of a finitely generated module
{synonym}
For a <finitely generated module> over a <principal ideal domain>, its invariant factors are nonzero nonunits $d_i$ in a decomposition $M\cong R^r\oplus\bigoplus_iR/(d_i)$, ordered by $d_i\mid d_{i+1}$. They are unique up to multiplication by units and describe the <torsion submodule>. Over $F[t]$, making $t$ act as a <linear operator> recovers the <invariant factors of a linear operator> used in its <rational canonical form>.
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