On similarity of matrices over commutative rings (Q1772732)

Let \(R\) be a commutative ring and let \(A\) be an \(n\times n\) matrix over \(R\). The author gives some direct criteria that determine when \(A\) is similar to its companion matrix or to a diagonal matrix over \(R\). He also gives conditions for the existence of a factorization \(A(x)= (xI_n- B)C(x)\) in the matrix ring \(R_{n,n}[x]\), \(x\) an indeterminant.