University of Guilan Journal of Algebra and Related Topics 2345-3931 6 2 2018 12 01 On the ranks of certain semigroups of order-preserving partial isometries of a finite chain 15 33 3327 10.22124/jart.2019.10875.1109 EN B. Ali Department of Mathematics, Nigeria Defence Academy, Kano, Nigeria M. A. Jada Department of Mathematics, Bayero University Kano, Kano, Nigeria M. M. Zubairu Department of Mathematics, Faculty of Physical Sciences, Bayero University, Kano, Nigeria Journal Article 2018 07 19 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 generated<br />subsemigroup $\langle N\rangle$ and the subsemigroup ~$L(n,r)= \{ \alpha \in \mathcal{ODP}_{n} : |im~\alpha|\leq r\}$. Order-Preserving partial transformations isometries height and right (left) waist idempotents and nilpotents https://jart.guilan.ac.ir/article_3327_56a79b622398bebb17cc02cf3f649d3b.pdf