Geodesic
Idempotence and regularity of generlized relational hypersubstitutions for algebraic sytems
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 369-382

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The concept of a generalized relational hypersubstitution for algebraic systems of type (τ,τ') is an extension of the concept of a generalized hypersubstitution for universal algebra of type τ. The set of all generalized relational hypersubstitutions for algebraic systems of type (τ,τ') together with a binary operation defined on the set and its identity forms a monoid. The properties of this structure are expressed by terms and relational terms. In this paper, we study the semigroup properties of the monoid of type ((n),(m)) for arbitrary natural numbers n,m ≥ 2. In particular, we characterize the idempotent as well as regular elements in this submonoid.
Keywords: generalized hypersubstitutions, algebraic systems, idempotent elements, regular elements 
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Kunama, Pornpimol; Leeratanavalee, Sorasak. Idempotence and regularity of generlized relational hypersubstitutions for algebraic sytems. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 369-382. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a8/