On substructures of semigroups of inductive terms

Pongsakorn Kitpratyakul; Bundit Pibaljommee; Pongsakorn Kitpratyakul; Bundit Pibaljommee

doi:10.3934/math.2022548

AIMS Mathematics

2022, Volume 7, Issue 6: 9835-9845. doi: 10.3934/math.2022548

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Research article

On substructures of semigroups of inductive terms

Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Received: 28 November 2021 Accepted: 14 March 2022 Published: 18 March 2022
MSC : 08A40, 08A70, 20M10

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.
- terms,
- semigroups,
- inductive composition of terms,
- subsemigroups,
- 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

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Abstract

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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