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