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Free Algebras of Full Terms Generated by Order-Preserving Transformations

Author

Listed:
  • Khwancheewa Wattanatripop

    (Department of Mathematics, Faculty of Science and Agricultural, Technology Rajamangala University of Technology Lanna, Chiang Mai 50300, Thailand
    These authors contributed equally to this work.)

  • Thodsaporn Kumduang

    (Department of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, Thailand
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Khwancheewa Wattanatripop & Thodsaporn Kumduang, 2025. "Free Algebras of Full Terms Generated by Order-Preserving Transformations," Mathematics, MDPI, vol. 13(9), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1433-:d:1644152
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    References listed on IDEAS

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    1. Klaus Denecke & Shelly L. Wismath, 2003. "Complexity of terms, composition, and hypersubstitution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-11, January.
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