Geodesic
On closed classes of polynomials over finite fields
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 50-62

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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. 
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     author = {A. P. Semigrodskikh and E. V. Sukhanov},
     title = {On closed classes of polynomials over finite fields},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
     volume = {9},
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     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a4/}
}
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A. P. Semigrodskikh; E. V. Sukhanov. On closed classes of polynomials over finite fields. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 50-62. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a4/