Geodesic
Closed classes of polynomials modulo $p^2$
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 54-69

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We consider functions of $p^2$-valued logic ($p$ is prime) that may be implemented by polynomials over the ring ${\mathbb Z}_{p^2}$, and describe all closed classes that contain linear functions. It turns out that the set of these classes is countable. We also construct the lattice of such classes with respect to inclusion.
Keywords: $k$-valued logic, closed class, clone, polynomials over a ring of residues, lattice of closed classes. 
@article{DM_2017_29_3_a4,
     author = {D. G. Meshchaninov},
     title = {Closed classes of polynomials modulo $p^2$},
     journal = {Diskretnaya Matematika},
     pages = {54--69},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_3_a4/}
}
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D. G. Meshchaninov. Closed classes of polynomials modulo $p^2$. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 54-69. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a4/