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

Document Type : Research Paper

Authors

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

2 Department of Mathematics and Computer Science, Borno State University, P. M. B. 1122, Njimtilo, Maiduguri, Nigeria

Abstract

‎Denote $[n]$ to be a finite $n$ chain $\{1,2,\ldots,n\}$‎. ‎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 $\mathcal{ODCI}_{n}$.‎

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References

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Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 127-153

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