Advanced Linear Algebra
《Advanced Linear Algebra》 · 第 157 页 · Chapter 6「The Invariant Factor Decomposition」，Theorem 6.16
Theorem 6.16 (The invariant factor decomposition theorem) Let $M$ be a finitely generated torsion module over a principal ideal domain $R$. Then $M=U_1\oplus\cdots\oplus U_r$, where $U_i$ is a cyclic submodule of $M$, with order $d_i$, where $d_1\mid d_2\mid\cdots\mid d_r$. This decomposition is called an invariant factor decomposition of $M$ and the scalars $d_i$ are called the invariant factors of $M$.