Representations of superassociative algebras by commutative functions with different types

Author:

Kumduang Thodsaporn1ORCID,Sriwongsa Songpon2

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, Thailand

2. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand

Abstract

For fixed integers [Formula: see text] and [Formula: see text], we study the faithful representation of superassociative algebras by two kinds of functions of the arity [Formula: see text], the so called [Formula: see text]-commutative and [Formula: see text]-commutative. The automorphism on the algebra of all [Formula: see text]-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 [Formula: see text]-commutative functions are isomorphic. With these results, a close connection with the theory of terms and tree languages is described.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Mathematics

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