Similarity of Matrices over Dedekind Rings

Abstract

We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent by a finite covering and verify this conjecture for $2\times 2$ matrices and separable characteristic polynomials.

19 pages, we have added some recent results, comments welcome!