Geodesic
Regular elements and Green's relations in Menger algebras of terms
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 1, pp. 85-109

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Defining an (n+1)-ary superposition operation S^n on the set W_τ(X_n) of all n-ary terms of type τ, one obtains an algebra n-clone τ := (W_τ(X_n); S^n, x_1, ..., x_n) of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation S^n there are different possibilities to define binary associative operations on the set W_τ(X_n) and on the cartesian power W_τ(X_n)^n. In this paper we study idempotent and regular elements as well as Green's relations in semigroups of terms with these binary associative operations as fundamental operations.
Keywords: term, superposition of terms, Menger algebra, regular element, Green's relations 
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Denecke, Klaus; Jampachon, Prakit. Regular elements and Green's relations in Menger algebras of terms. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 1, pp. 85-109. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_1_a4/