On the Latimer-MacDuffee theorem for polynomials over finite fields
Van Zyl, Jacobus Visser · 2011
On the Latimer-MacDuffee theorem for polynomials over finite fields J.V. van Zyl Department of Mathematics and Applied Mathematics, Rhodes University, Grahamstown 6140, South Africa. Dissertation: PhD (Mathematics) March 2011 Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. In the case where the matrices are taken over the integers, Behn and Van der Merwe developed an algorithm in 2002 to produce a representative in each equivalence class. We extend this algorithm to matrices taken over the ring Fq[T ] of polynomials over a finite field and prove a modified version of the Latimer-MacDuffee theorem which holds for proper equivalence classes of matrices.