FUZZY SEMIGROUPS IN REDUCTIVE SEMIGROUPS

Abstract. We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that S(k) = 1 for some k ∈ X and find a faithful representation (or anti-representation) of S by transfor-mations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that S(k) = 1 for some k ∈ X is isomor-phic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup. 1