@article {7088,
	title = {A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutations},
	journal = {Bull. Korean Math. Soc.},
	volume = {53},
	year = {2016},
	pages = {495-506},
	abstract = {<p>In this note we consider the monoid $PODI_n$ of all monotone partial permutations on $\{1,\ldots,n\}$ and its submonoids $DP_n$, $POI_n$ and $ODP_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $POI_n$ and $ODP_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $PODI_n$ is a quotient of a semidirect product of $POI_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $DP_n$ is a quotient of a semidirect product of $ODP_n$ and $\mathcal{C}_2$. </p>
},
	url = {http://pdf.medrang.co.kr/kms01/BKMS/53/BKMS-53-2-495-506.pdf},
	author = {Fernandes, V{\'\i}tor H. and Quinteiro, Teresa M.}
}
