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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.

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