@article {
author = {Ali, B. and Jada, M. A. and Zubairu, M. M.},
title = {On the ranks of certain semigroups of order-preserving partial isometries of a finite chain},
journal = {Journal of Algebra and Related Topics},
volume = {6},
number = {2},
pages = {15-33},
year = {2018},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {10.22124/jart.2019.10875.1109},
abstract = {Let $X_n=\{1,2,\ldots,n\}$ be a finite chain, $\mathcal{ODP}_{n}$ be the semigroup of order-preserving partial isometries on $X_n$ and $N$ be the set of all nilpotents in $\mathcal{ODP}_{n}$. In this work, we study the nilpotents in $\mathcal{ODP}_{n}$ and investigate the ranks of two subsemigroups of $\mathcal{ODP}_{n}$; the nilpotent generatedsubsemigroup $\langle N\rangle$ and the subsemigroup ~$L(n,r)= \{ \alpha \in \mathcal{ODP}_{n} : |im~\alpha|\leq r\}$.},
keywords = {Order-Preserving partial transformations,isometries,height and right (left) waist,idempotents and nilpotents},
url = {https://jart.guilan.ac.ir/article_3327.html},
eprint = {https://jart.guilan.ac.ir/article_3327_56a79b622398bebb17cc02cf3f649d3b.pdf}
}