Clones sous-maximaux des Polymorphismes d’une relation d’équivalence non triviale contenant les fonctions unaires

Abstract

Let k ∈ Nsuch that k ≥ 3, θ a nontrivial equivalence relation on Ek ∶= {0,..., k−1} with t classes. It is known from Rosenberg’s classification theorem ( 1965) that the clone Polθ (of operations on Ek preserving θ) is a maximal clone in the inclusion-ordered lattice of clones on Ek. We denote by Pol(1) θ the set of all unary operations of Polθ. In this work ;we characterize some maximal elements of the interval of clone [Pol(1)θ,Polθ] and describe some chains of this interval.