# Binary systems of full terms arising from some mappings

## Main Article Content

## Abstract

Full terms with an invariant set are special types of terms defined by full transformations with an invariant set on a finite set and variables from an alphabet applied in the theory of solid varieties. The set of all full terms with an invariant set is closed under the superposition operation under which the superassociative law holds. This work introduced three different binary operations on the set of all full terms with an invariant set and proves associativity. Moreover, tree languages of full terms with an invariant set and their operations were considered. Finally, embedding theorems of semigroups of full terms with an invariant set into semigroups of tree languages of full terms with an invariant set were proposed.

## Article Details

*RMUTSB ACADEMIC JOURNAL*,

*11*(2), 149–158. Retrieved from https://li01.tci-thaijo.org/index.php/rmutsb-sci/article/view/258693

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Published manuscript are the rights of their original owners and RMUTSB Academic Journal. The manuscript content belongs to the authors' idea, it is not the opinion of the journal's committee and not the responsibility of Rajamangala University of Technology Suvarnabhumi

## References

Chansuriya, N. (2021). All maximal idempotent submonoids of generalized cohypersubstitutions of type τ=(2). Discussiones Mathematicae - General Algebra and Applications, 41(1), 45-54.

Chinram, R., & Baupradist, S. (2019). Magnifying elements of semigroups of transformations

with invariant set. Asian-European Journal of Mathematics, 12(4), 1950056.

Denecke, K. (2016). The partial clone of linear terms. Siberian Mathematical Journal, 57(4), 589-598.

Denecke, K. (2022). Partial Menger algebras and their weakly isomorphic representation. Mathematics Open, 1, 2250003.

Denecke, K., & Hounnon, H. (2021). Partial Menger algebras of terms. Asian-European Journal of Mathematics, 14(6), 2150092.

Denecke, K., & Jampachon, P. (2003). Clones of full terms. Algebra and Discrete Mathematics, 4, 1-11.

Dudek, W. A., & Trokhimenko, V. S. (2021). Menger algebras of k-commutative n-place functions. Georgian Mathematical Journal, 28(3), 355-361.

Honyam, P., & Sanwong, J. (2011). Semigroups of transformations with invariant set. Journal of the Korean Mathematical Society, 48(2), 289-300.

Joomwong, J., & Phusanga, D. (2021). On Green’s relations which are related to an algebraic system of Type (m,n). Southeast Asian Bulletin of Mathematics, 45(6), 897-904.

Kumduang, T., & Sriwongsa, S. (2022). A note on superassociative algebra of terms determined by singular mappings on a finite set. International Journal of Mathematics and Computer Science, 14(4), 1541-1546.

Lekkoksung, N., & Lekkoksung, S. (2021). On partial clones of k-terms. Discussiones Mathematicae - General Algebra and Applications, 41(2), 361-379.

Phuapong, S., & Kumduang, T. (2021). Menger algebras of terms induced by transformations with restricted range. Quasigroups and Related Systems, 29, 255-268.

Phuapong, S., & Pookpienlert, C. (2022). S(n_i,Y_i)-terms and their algebraic properties. Thai Journal of Mathematics, 20(1), 337-346.

Salehia, S., & Steinby, M. (2007). Tree algebras and varieties of tree languages. Theoretical Computer Science, 377, 1-24.

Sarkar, M., & Singh, S. N. (2022). On certain semigroups of transformations with an invariant set. Asian-European Journal of Mathematics, 15(11), 2250198.

Wattanatripop, K., & Changphas, T. (2019). The clone of K* (n,r)-full terms. Discussiones Mathematicae - General Algebra and Applications, 39(2), 277-288.

Wattanatripop, K., & Changphas, T. (2021a). On nd-K* (n,r)-Full hypersubstitutions. Discussiones Mathematicae - General Algebra and Applications, 41(2), 213-227.

Wattanatripop, K., & Changphas, T. (2021b). The Menger algebra of terms induced by order-decreasing Transformations. Communications in Algebra, 49(7), 3114-3123.