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 any mi-ary operation symbol to an mi-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 the monoid 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)), where m, n ≥ 2.