Classification of the functions over primary ring of residues considered in connection with the method of coordinate linearization

It's known that the method of coordinate linearization may be used for solving a system of polynomial equations over primary ring of residues. Here, some classification is made for functions over primary ring of residues providing systems of equations which may be solved by using this method. The class of polynomial functions is extended to class of variative-coordinate polynomial functions (VCP-functions) which is also extended to the class of quasi-VCP-functions and to the class of coordinate-linear solvable functions. Properties of these classes are described.