The uniform $id$-decomposition of functions of many-valued logic over homogeneous functions

We consider the uniform $id$-decomposition of functions of the class $P_k$ of functions of $k$-valued logic over the class $H^*_k$ of structural homogeneous functions and the class $D_k$ of homogeneous functions generated by the dual discriminator $d$. We find the degrees of the uniform $id$-decomposition of the class $P_k$ over the classes $H^*_k$ and $D_k$ and give the methods of construction of homogeneous functions over which the uniform $id$-decomposition of the class $P_k$ is realised.