On the ranks of certain semigroups of order-preserving partial isometries of a finite chain
Publish place: The Journal of Algebra and Related Topics، Vol: 6، Issue: 2
Publish Year: 1397
Type: Journal paper
Language: English
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Document National Code:
JR_JART-6-2_002
Index date: 21 July 2024
On the ranks of certain semigroups of order-preserving partial isometries of a finite chain 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\}.
On the ranks of certain semigroups of order-preserving partial isometries of a finite chain Keywords:
Order-Preserving partial transformations , isometries , height and right (left) waist , idempotents and nilpotents
On the ranks of certain semigroups of order-preserving partial isometries of a finite chain authors
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
