On Some Algebraic Properties of Order-Preserving Full Contraction Transformation Semigroup

Abstract

Let Xn be a finite set, CTn the semigroup of full contraction and OCTn order-preserving full contraction transformation semigroup of a finite set. In this paper the Local and global U-depth as well as the status of OCTn were investigated where U is the generating set. The local and global depth were found from the known generating Set of OCTn and also, the status of the semigroup OCTn was obtained from the product of global depth and the order of generating of OCTn. For a 2 OCTn, local depth of is equal to its defect, global depth and status of OCTn are n􀀀1 and 2(n􀀀1)2 respectively. We also look at the structure of Greens relations of order-preserving full contraction transformation semigroup.