Geodesic
The monoid of generalized hypersubstitutions of type τ = (n)
Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 173-191

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A (usual) hypersubstitution of type τ is a function which takes each operation symbol of the type to a term of the type, of the same arity. The set of all hypersubstitutions of a fixed type τ forms a monoid under composition, and semigroup properties of this monoid have been studied by a number of authors. In particular, idempotent and regular elements, and the Green's relations, have been studied for type (n) by S.L. Wismath.
Keywords: monoid, regular elements, idempotent elements, Green's relations, generalized hypersubstitution 
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Puninagool, Wattapong; Leeratanavalee, Sorasak. The monoid of generalized hypersubstitutions of type τ = (n). Discussiones Mathematicae. General Algebra and Applications, Tome 30 (2010) no. 2, pp. 173-191. http://geodesic.mathdoc.fr/item/DMGAA_2010_30_2_a2/