Geodesic
The structure of the lattice of closed classes of polynomials
Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 24-39

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In this article the structure of the lattice of closed classes of polynomials modulo $k$ is investigated. More precisely, we investigate the structure of the interval of this lattice from the class of all linear polynomials with zero constant term to the class of all polynomials modulo $k$. It is proved that this interval (as partially ordered set) is the direct product of two subintervals, and its structure is completely determined when $k$ is square free. Moreover, for $k=4$ (minimal not square free $k$) the description of the interval from the class of all linear polynomials to the class of all polynomials is given. 
@article{DM_1997_9_2_a2,
     author = {A. A. Krokhin and K. L. Safin and E. V. Sukhanov},
     title = {The structure of the lattice of closed classes of polynomials},
     journal = {Diskretnaya Matematika},
     pages = {24--39},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_2_a2/}
}
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A. A. Krokhin; K. L. Safin; E. V. Sukhanov. The structure of the lattice of closed classes of polynomials. Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 24-39. http://geodesic.mathdoc.fr/item/DM_1997_9_2_a2/