Generalized equivalence of collections of matrices and common divisors of matrices

The collections $(A_{1},\dots, A_{k})$ and $(B_{1},\dots, B_{k})$ of matrices over an adequate ring are called generalized equivalent if $A_i=UB_iV_i$ for some invertible matrices $U$ and $V_{i}, \; i=1,\dots, k$. Some conditions are established under which the finite collection consisting of the matrix and its the divisors is generalized equivalent to the collection of the matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices is described.