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

Let X_n=\{۱,۲,\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\}.

کلیدواژه ها:

Order-Preserving partial transformations ، isometries ، height and right (left) waist ، idempotents and nilpotents