Geodesic
Congruence preserving operations on the ring $\mathbb {Z}_{p^3}$
Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 519-535.

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We investigate the interval $I(p^3)$ in the lattice of clones on the ring $\mathbb {Z}_{p^3}$ between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this paper, we characterize each of these clones by the property of preserving a small set of relations. These relations turn out to be in a close connection to commutators.
DOI : 10.21136/MB.2022.0155-21
Classification : 03B50, 08A40
Keywords: congruence; clone; polynomial 
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Gavala, Cyril; Ploščica, Miroslav; Varga, Ivana. Congruence preserving operations on the ring $\mathbb {Z}_{p^3}$. Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 519-535. doi : 10.21136/MB.2022.0155-21. http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0155-21/

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