Geodesic
Some families of closed classes in~$P_k$ defined by additive formulas
Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 100-116

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We analyse closed classes in $k$-valued logics containing all linear functions modulo $k$. The classes are determined by divisors $d$ of a number $k$ and canonical formulas for functions. We construct the lattice of all such classes for $k=p^2$, where $p$ is a prime, and construct fragments of the lattice for other composite $k$.
Keywords: function algebra, $k$-valued logic, lattice of closed classes, linear function. 
@article{DM_2021_33_2_a7,
     author = {D. G. Meshchaninov},
     title = {Some families of closed classes in~$P_k$ defined by additive formulas},
     journal = {Diskretnaya Matematika},
     pages = {100--116},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_2_a7/}
}
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D. G. Meshchaninov. Some families of closed classes in~$P_k$ defined by additive formulas. Diskretnaya Matematika, Tome 33 (2021) no. 2, pp. 100-116. http://geodesic.mathdoc.fr/item/DM_2021_33_2_a7/