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

Denecke K., Glubudom P.

Demonstratio Mathematica

2008

Vol. 41, nr 1

11-22

Sets of terms of type r are called tree languages (see [5]). On sets of tree languages superposition operations can be defined in such a way that the collection of all tree languages of type r forms an abstract clone. Considering only sets of n-ary terms one obtains a Menger algebra (see e.g. [3]). From the superposition operations binary operations on tree languages can be derived. For the corresponding sernigroups of tree languages we study idempotent and regular elements as well as Green's relations L and R.