  The problem of a differential operator left- and right division is solved in
terms of generalized Bell polinomials for nonabelian differential unitary ring.
The definition of the polinomials is made by means of recurrent relations. The
expresions of classic Bell polinomils via generalized one is given. The
conditions of an exact factorization possibility leads to the intertwine
relation and results in some linearizable generalized Burgers equation. An
alternative proof of the Matveev theorem is given and Darboux - Matveev
transformations formula for coefficients follows from the intertwine relations
and also expressed in the generalized Bell polinomials.
