arXiv subjects
Publications and source records attributed to Etienne R. A. Temgoua.
Let rho and sigma be two central relations on a finite set A. It is known that the clones Pol(rho) and Pol(sigma) which consists of all operations on A that preserve rho respectively sigma are among the maximal clones on A. In this paper, we find all central relations sigma such that the join clone of Pol(rho) and Pol(sigma) is a maximal subclone of Pol(rho) where rho is a fixed central relation.
The structure of the lattice of clones on a finite set has been proven to be very complex. To better understand the top of this lattice, it is important to provide a characterization of submaximal clones in the lattice of clones. It is known that the clones $Pol(θ)$ and $Pol(ρ)$ (where $θ$ is a nontrivial equivalence relation on $E_k = \{0,\dots, k-1\}$, and $ρ$ is among the six types of relations which characterize maximal clones) are maximal clones. In this paper, we provide a classification of relations (of Rosenberg's List) on $E_k$ such that the clone $Pol(θ) \cap Pol(ρ)$ is maximal in $Pol(θ)$.