MEET-REDUCIBLE SUBMAXIMAL CLONES DETERMINED BY NONTRIVIAL EQUIVALENCE RELATIONS
Luc E. F. Diekouam, Yannick Léa Tenkeu Jeufack, Etienne R. A. Temgoua, Marcel Tonga · Journal of Algebra Number Theory Advances and Applications · 2017
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 ( ) θ Pol and ( ) ρ Pol (where θ is a nontrivial equivalence relation on { } , 1 , , 0 -= k k … E and ρ belongs to one of 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) ρ on k E for which the clone ( ) ( ) ρ θ Pol Pol ∩ is maximal inPol θ