Latimer–MacDuffee theorem

The Latimer–MacDuffee theorem is a theorem in abstract algebra, a branch of mathematics. It is named after Claiborne Latimer and Cyrus Colton MacDuffee, who published it in 1933. Significant contributions to its theory were made later by Olga Taussky-Todd.

Let ${\displaystyle f}$ be a monic, irreducible polynomial of degree ${\displaystyle n}$. The Latimer–MacDuffee theorem gives a one-to-one correspondence between ${\displaystyle \mathbb {Z} }$-similarity classes of ${\displaystyle n\times n}$ matrices with characteristic polynomial ${\displaystyle f}$ and the ideal classes in the order

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