On Collapse Of Order-Preserving and Idempotent of Order-Preserving FullContraction Transformation Semigroup

Abstract

Let Tn be the set of full transformation semigroup on Xn = {1, 2, 3, · · · , n}, C +(α) =|OCTn |= q be it’s subsemigroup on collapse of order-preserving full contraction transformation, C +(αE) =| E(OCTn) |= qE be the collapse on idempotent of order-preserving full contraction transformation and C +(α) =| C +(α) |= ∪t∈Imα | {tα−1 ≥ 2} | be the formula for total number of collapsible element.In this paper, we investigate the collapse element on order-preserving and idempotent of order-preserving full contraction transformation semigroup.