Thodsaporn Kumduang – Menger Algebras of Weak Near-unanimity n-ary operations

Chiang Mai University, Thailand
Various fields in mathematics have to consider multiplace functions, which are also called functions of many variables, and its algebras called Menger algebras. The primary aim of this paper is to present two specific types of $n$-ary operations which are called cyclic and weak near-unanimity using the concepts of cyclic and weak near-unanimity terms in the study of universal algebra, respectively. The Menger algebras of these two $n$-ary operations defined on a fixed set are constructed and some algebraic properties are investigated. In particular, we provide the necessary and sufficient conditions under which an abstract Menger algebra can be isomorphically represented by such $n$-ary operations.