| Abstrakt: |
For fixed integers 1 ≤ i < j ≤ n and σ ∈ S n , we study the faithful representation of superassociative algebras by two kinds of functions of the arity n , the so called (i , j) -commutative and σ -commutative. The automorphism on the algebra of all (i , j) -commutative functions is determined. In general, an isomorphism from a superassociative system which consists of a family of nonempty sets and a family of operations satisfying the axiom of superassociativity to a system of full multiplace functions is discussed. Particularly, we also provide necessary and sufficient conditions under which a superassociative system and a system of σ -commutative functions are isomorphic. With these results, a close connection with the theory of terms and tree languages is described. [ABSTRACT FROM AUTHOR] |
