@article {470,
	title = {Bilateral semidirect product decompositions of transformation monoids.},
	journal = {Semigroup Forum},
	volume = {82},
	number = {2},
	year = {2011},
	pages = {271-287},
	abstract = {Summary: In this paper we consider the monoid $\mathcal {OR}_{n}$ of all full transformations on a chain with $n$ elements that preserve or reverse the orientation, as well as its submonoids $\mathcal {OD}_{n}$ of all order-preserving or order-reversing elements, $\mathcal {OP}_{n}$ of all orientation-preserving elements and $\mathcal {O}_{n}$ of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirect product of two of its remarkable submonoids.},
	keywords = {bilateral semidirect products, free monoids, presentations, transformation semigroups},
	doi = {10.1007/s00233-011-9290-1},
	author = {Fernandes, V{\'\i}tor H. and Quinteiro, Teresa M.}
}
