Turkish Journal of Mathematics
DOI
10.3906/mat-1602-52
Abstract
Let $X_{n}=\{1,2,\ldots,n\}$ with its natural order and let ${\cal T}_{n}$ be the full transformation semigroup on $X_{n}$. A map $\alpha\in{\cal T}_{n}$ is said to be order-preserving if, for all $x,y\in X_{n}$, $x\leq y\Rightarrow x\alpha\leq y\alpha$. The map $\alpha\in{\cal T}_{n}$ is said to be a contraction if, for all $x,y\in X_{n}$, $ x\alpha-y\alpha \leq x-y $. Let ${\cal CT}_{n}$ and ${\cal OCT}_{n}$ denote, respectively, subsemigroups of all contraction maps and all order-preserving contraction maps in ${\cal T}_{n}$. In this paper we present characterisations of Green's relations on ${\cal CT}_{n}$ and starred Green's relations on both ${\cal CT}_{n}$ and ${\cal OCT}_{n}$.
Keywords
Full transformation, order-preserving, contraction, Green's relations, starred Green's relations
First Page
500
Last Page
507
Recommended Citation
GARBA, GOJE UBA; IBRAHIM, MUHAMMAD JAMILU; and IMAM, ABDUSSAMAD TANKO
(2017)
"On certain semigroups of full contraction maps of a finite chain,"
Turkish Journal of Mathematics: Vol. 41:
No.
3, Article 3.
https://doi.org/10.3906/mat-1602-52
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss3/3
