A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations - Petrichkovich, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent.