Idempotent of Weak Projection Cohypersubstitutions

Nareupanat Lekkoksung, Prakit Jampachon, Somsak Lekkoksung

Abstract

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.