Fillmore's theorem for matrices over factorial rings.

Fillmore's Theorem says that if A is a nonscalar matrix of order n over a field F and γ 1 , γ 2 , ... , γ n ∈ F are such that γ 1 + γ 2 + ⋯ + γ n = t r A , then there is a matrix B of order n over F similar to A with diagonal (γ 1 , γ 2 , ... , γ n). Borobia extended Fillmore's Theorem to the matrices over the ring Z of integers. In this paper, we will extend Fillmore's Theorem to the matrices over a general factorial ring. [ABSTRACT FROM AUTHOR]