# Clones containing the Mal'cev operation of $\mathbb{Z}_{pq}$

@article{Fioravanti2020ClonesCT, title={Clones containing the Mal'cev operation of \$\mathbb\{Z\}\_\{pq\}\$}, author={Stefano Fioravanti}, journal={arXiv: Rings and Algebras}, year={2020} }

We investigate finitary functions from $\mathbb{Z}_{pq}$ to $\mathbb{Z}_{pq}$ for two distinct prime numbers $p$ and $q$. We show that the lattice of all clones on the set $\mathbb{Z}_{pq}$ which contain the addition of $\mathbb{Z}_{pq}$ is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattice of all $(\mathbb{Z}_p,\mathbb{Z}_q)$-linearly closed clonoids to the $p+1$ power and the lattice of all $(\mathbb{Z}_q…

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