Some algebraic properties of order-preserving full contraction transformation semigroup

Abstract

Let $X_{n}$ be a finite set, $CT_{n}$ the semigroup of full contraction and $OCT_{n}$ 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 $OCT_{n}$ were investigated where U is the generating set. The local and global depth were found from the known generating Set of $OCT_{n}$ and also, the status of the semigroup $OCT_{n}$ was obtained from the product of global depth and the order of generating of $OCT_{n}$. For $\alpha\in OCT_{n}$, local depth of α is equal to its defect, global depth and status of $OCT_{n}$ are $ n-1$ and $2(n-1)^{2}$ respectively. We also look at the structure of Green’s relations of order-preserving full contraction transformation semigroup.