Free Algebras of Full Terms Generated by Order-Preserving Transformations

Khwancheewa Wattanatripop and Thodsaporn Kumduang ()
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Khwancheewa Wattanatripop: Department of Mathematics, Faculty of Science and Agricultural, Technology Rajamangala University of Technology Lanna, Chiang Mai 50300, Thailand
Thodsaporn Kumduang: Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, Thailand

Mathematics, 2025, vol. 13, issue 9, 1-21

Abstract: Full terms, which serve as tools for classifying algebras into subclasses, can be studied using an algebraic approach. For a natural number n , this paper introduces the algebra of order-preserving full terms under the ( n + 1 ) -superposition operation satisfying the superassociativity using mappings on the set O n of all order-preserving transformations on a finite chain { 1 ≤ ⋯ ≤ n } . We prove the freeness property of such algebra with respect to the variety of superassociative algebras. Additionally, binary operations on the powerset of order-preserving full terms whose elements are called tree languages are discussed. To define order-preserving identities and order-preserving varieties, the left-seminearring of full hypersubstitutions is determined. The required characteristics for any identity to be an order-preserving identity are considered. Furthermore, we also discuss the homomorphism of full hypersubstitutions with other algebraic structures.

Keywords: free algebra; full term; transformation; homomorphism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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