Work

Free Algebras of Full Terms Generated by Order-Preserving Transformations

Year: 2025

Type: article

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 On 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.

Source: Mathematics

DOI: 10.3390/math13091433

Authors: Khwancheewa Wattanatripop, Thodsaporn Kumduang

Institutions: Rajamangala University of Technology Lanna, Rajamangala University of Technology Rattanakosin

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Research Council of Thailand