Green’s Relations on Regular Elements of Semigroup of Relational Hypersubstitutions for Algebraic Systems of Type ((m), (n))

Abstract

Any relational hypersubstitution for algebraic systems of type (τ, τ ′) = ((mi)i∈I , (nj)j∈J) is a mapping which maps anymi-ary operation symbol to anmi-ary term and maps any njary relational symbol to an nj-ary relational term preserving arities, where I, J are indexed sets. Some algebraic properties of themonoid of all relational hypersubstitutions for algebraic systems of a special type, especially the characterization of its order and the set of all regular elements, were first studied by Phusanga and Koppitz[13] in 2018. In this paper, we study the Green’s relations on the regular part of this monoid of a particular type (τ, τ ′) = ((m), (n)), wherem,n ≥ 2.