On closed classes of polynomials over finite fields

The structure of the lattice of closed classes of $k$-valued functions is studied. Let $F$ be the class of all polynomials over a field of $k=p^n$ elements, and let $L^0$ be the class of linear forms over this field. The paper gives a complete description of all closed classes lying in the indicated lattice between $L^0$ and $F$. In particular, (finite) bases of such classes are given.