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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 54

Partial Algebras of Formulas Under Generalized Superpositions

Author(s)

T. Kumduang1,  K. Wattanatripop2

1 Rajamangala University of Technology Rattanakosin, Nakhon Pathom, Thailand

2 Rajamangala University of Technology Lanna, Chiang Mai, Thailand

Abstract
Formulas which are tools for describing algebraic systems are formal expressions arising from terms, relation symbols, and logical connectives. Under composition of the generalized superposition operation, the set of all terms forms a unitary superassociative algebra. This paper deals with construction of the partial generalized superposition on the set of all terms and formulas satisfying the superassociativity as a weak identity. Partial binary operations induced by such partial generalized superpositions are given and the fact that these operations are weak associative are proved.
About the Authors

T. Kumduang, Ph. D. (Math.), Lecturer, Rajamangala University of Technology Rattanakosin, Nakhon Pathom, 73170, Thailand, thodsaporn.kum@rmutr.ac.th

K. Wattanatripop, Ph. D. (Math.), Lecturer, Rajamangala University of Technology Lanna, Chiang Mai, 50300, Thailand, khwancheewa.wat@rmutl.ac.th

For citation
Kumduang T., Wattanatripop K. Partial Algebras of Formulas Under Generalized Superpositions. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 54, pp. 160–175. https://doi.org/10.26516/1997-7670.2025.54.160
Keywords
partial algebra, formula, term, superassociativity, partial semigroup, weak
UDC
512.577
MSC
08A02, 08A05, 08A70, 20N02, 20N15
DOI
https://doi.org/10.26516/1997-7670.2025.54.160
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