Czechoslovak Mathematical Journal, first online, pp. 1-10


Presentations for subsemigroups of $PD_n$

Abdullahi Umar

Received July 23, 2017.   Published online August 9, 2018.

Abstract:  Let $[n]=\{1,\ldots,n\}$ be an $n$-chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-decreasing mappings of $[n]$, the semigroup of full order-preserving and order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-preserving and order-decreasing mappings of $[n]$, and the semigroup of partial order-preserving and order-decreasing mappings of $[n]$.
Keywords:  presentation; order-decreasing mapping; order-preserving mapping; transformation semigroups
Classification MSC:  20M20, 20M30
DOI:  10.21136/CMJ.2018.0343-17

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Affiliations:   Abdullahi Umar, Department of Mathematical Sciences, Petroleum Institute, P. O. Box 2533, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates, e-mail: aumar@pi.ac.ae


 
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