Abstract
In this paper, we define terms generated by transformations preserving a partition on a finite set and then construct their superassociative structures. A generating system of such algebra is determined and the freeness in a variety of all superassociative algebras is investigated. The connection between a semigroup of all mappings whose ranges are terms induced by transformations preserving a partition and substitutions is discussed. In views of applications, we apply these mappings to examine identities of a variety in a higher step. Additionally, we generalize our study to algebraic systems and establish a superassociative algebra of a new type of formulas induced by terms defined by transformations preserving a partition.
Acknowledgement
The first author acknowledges support by Rajamangala University of Technology Rattanakosin, Thailand. The authors would like to express their gratitude to the referees for their valuable comments and suggestions.