On substructures of semigroups of inductive terms

Abstract

<abstract><p>An inductive composition is an operation generalizing from a superposition $ S^n $ on the set of all $ n $-ary terms of type $ \tau $. A binary operation called <italic>inductive product</italic> is obtainable from such composition. It is a generalization of a tree language product but on the set of all $ n $-ary terms of type $ \tau $. Unlike the original one, this inductive product is not associative on the mentioned set. Nonetheless, it turns to be associative on some restricted set. A semigroup arising in this way is the main focus of this paper. We consider its special subsemigroups and semigroup factorizations.</p></abstract>

Algebras of generalized tree languages with fixed variables

“…The set of all variables that appear in t is denoted by var(t). More background and current trends in the investigation of terms may be found in [5,13,18].…”