Idempotent of Weak Projection Cohypersubstitutions: Nareupanat Lekkoksung, Prakit Jampachon, Somsak Lekkoksung - Team, Support (Thai Journal of Mathematics, 2023)
K. Denecke and K. Saengsura established a Galois-connection between monoids of cohypersubstitutuions of a given type τ and varieties of the same type, showing that for any monoid M of cohypersubstitutions of type τ , the collection of all M-solid varieties of type τ forms a complete sublattice of the lattice of all varieties ([1]). It is of interest to know which semigroup properties of cohypersubstitutions can be transferred by this Galois connection. In this paper, we study the semigroup properties of weak projection cohypersubstitutions of all mappings from the set of cooperation symbols to the set of coterms which preserve arities type (2, 2). In particular, we characterize all idempotent elements of such cohypersubstitutions.