Let finite chain, and let denote the semigroup of full contraction transformations on . In this study, we investigate structural properties of , with particular emphasis on characterization, rank and defect, and Idempotent elements of Also, principal theorems were proved. A contraction transformation is a mapping satisfying for all . We establish the foundational structure for studying these properties and identify the results that require independent characterization for .
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Garba et al. (2026) studied this question.
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