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 inductive product 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.
Citation: Pongsakorn Kitpratyakul, Bundit Pibaljommee. On substructures of semigroups of inductive terms[J]. AIMS Mathematics, 2022, 7(6): 9835-9845. doi: 10.3934/math.2022548
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 inductive product 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.
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Pongsakorn Kitpratyakul, Bundit Pibaljommee. On substructures of semigroups of inductive terms[J]. AIMS Mathematics, 2022, 7(6): 9835-9845. doi: 10.3934/math.2022548
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