Superassociative structures of terms and formulas defined by transformations preserving a partition

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.

Keywords:

• Formula
• superassociativity
• term
• transformation
• variety

2020 Mathematics Subject Classification:

• 03C05
• 08A02
• 20M35
• 68Q70

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.

Additional information

Funding

This research was supported by King Mongkut’s University of Technology Thonburi (KMUTT) under the Postdoctoral Fellowship.