Let 3, .., n} and be a transformation from whereThe semigroup of (the full transformation semigroup), (the partial transformation semigroup) and (the partial one – one transformation semigroup) serve the bedrock for these transformation semigroups, Let denotes the sets of signed full order – preserving, signed partial order – preserving and signed partial one – one order – preserving transformation semigroup respectively. The paper aims at investigate the sets of these subsemigroups.
Keywords: Chain Decomposition, Idempotent, Nilpotent, Order Preserving, Self-Inverse, Transformation Semigroup
