On the maximal subsemigroups and rank properties of certain semigroups of partial injective contractions of a finite chain

‎Denote [n] to be a finite n chain \{۱,۲,\ldots,n\}‎. ‎Let \mathcal{CI}_{n} be the semigroup of partial injective contractions on [n]‎. ‎Denote \mathcal{ODDP}_{n}‎, ‎\mathcal{ODCI}_{n} and \mathcal{OCI}_{n} to be the semigroups of order-preserving order-decreasing partial isometries‎, ‎order-preserving order-decreasing and order-preserving partial injective contractions‎, ‎respectively‎. ‎In this paper‎, ‎we characterize all the maximal subsemigroups of \mathcal{ODDP}_{n}‎, ‎\mathcal{ODCI}_{n} and \mathcal{OCI}_{n}‎, ‎respectively‎. ‎We also characterize the regular elements‎, ‎Green's relations‎, ‎their Starred analogues and rank properties of \mathcal{ODCI}_{n}.‎

کلیدواژه ها:

Partial injective Contraction maps on chain ، maximal subsemigroups ، rank properties