@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.} }