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- Title
ALGEBRAS OF LEFT VARIABLE TERMS.
- Authors
Sungtong, Nuthawud; Kumduang, Thodsaporn; Phuapong, Sarawut
- Abstract
Terms are fundamental notions in universal algebra for describing algebraic properties and classifying algebras. In this paper, we propose the concept of a specific class of terms which are either variables or composed terms where the first input of terms is an arbitrary variable. In this situation, we call such term that a left variable term. Particularly, we define the partial many-sorted superposition operation on the set of such terms and construct the partial many sorted algebras, called the partial clone of left variable terms, satisfying the superassotive law. Based on the idea of clones, algebraic structures consisting a set of operations with compositions of operations and projection mappings, the partial many-sorted superposition operation is defined on sets of left variable term operations and its properties are given. We also present the notion of term operations on left variable terms and study some important properties. Finally, a hypersubstitution which takes any operation symbol to a left variable term of the corresponding arity is considered. Several properties of such hypersubstitution are examined and it turns out that the collection of them forms a partial monoid under a suitable partial binary associative operation.
- Subjects
UNIVERSAL algebra; ALGEBRA; BINARY operations; MAP projection; MONOIDS
- Publication
Palestine Journal of Mathematics, 2023, Vol 12, Issue 1, p946
- ISSN
2219-5688
- Publication type
Article