Latimer–MacDuffee theorem

Latimer-MacDuffee theorem is a theorem in abstract algebra, a branch of mathematics.

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

$\mathbb {Q} [x]/(f(x)).$

References

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