On the ranks of certain semigroups of order-preserving partial isometries of a finite chain

Document Type : Research Paper

Authors

1 Department of Mathematics, Nigeria Defence Academy, Kano, Nigeria

2 Department of Mathematics, Bayero University Kano, Kano, Nigeria

3 Department of Mathematics, Faculty of Physical Sciences, Bayero University, Kano, Nigeria

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 generated
subsemigroup $\langle N\rangle$ and the subsemigroup ~$L(n,r)= \{ \alpha \in \mathcal{ODP}_{n} : |im~\alpha|\leq r\}$.

Keywords

Journal of Algebra and Related Topics
Volume 6, Issue 2
December 2018
Pages 15-33

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