Regular elements and Green's relations in Menger algebras of terms

Klaus Denecke, Prakit Jampachon
2006 Discussiones Mathematicae - General Algebra and Applications  
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
more » ... ements as well as Green's relations in semigroups of terms with these binary associative operations as fundamental operations.
doi:10.7151/dmgaa.1106 fatcat:2ylcr6ulprhvpbk6qjfberaphu