Latimer–MacDuffee theorem

Let $f$ be a monic, irreducible polynomial of degree $n$. The Latimer-MacDuffee Theorem gives a one-to-one correspondance between $\mathbb {Z}$-similarity classes of $n\times n$ matrices with characteristic polynomial $f$ and the ideal classes of the ring $\mathbb {Q} [x]/(f(x))$

Sources

• A Correspondence Between Classes of Ideals and Classes of Matrices, by Claiborne G. Latimer; C. C. MacDuffee The Annals of Mathematics. 1933.