Binary systems of full terms arising from some mappings
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Abstract
Full terms with an invariant set are special types of terms defined by full transformations with an invariant set on a finite set and variables from an alphabet applied in the theory of solid varieties. The set of all full terms with an invariant set is closed under the superposition operation under which the superassociative law holds. This work introduced three different binary operations on the set of all full terms with an invariant set and proves associativity. Moreover, tree languages of full terms with an invariant set and their operations were considered. Finally, embedding theorems of semigroups of full terms with an invariant set into semigroups of tree languages of full terms with an invariant set were proposed.
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