Fernandes, Vítor H.Quinteiro, Teresa2013-01-302013-01-302011-04FERNANDES, Vítor H.; QUINTEIRO, Teresa M. - Bilateral semidirect product decompositions of transformation monoids. Semigroup Forum. ISSN 0037-1912. Vol. 82, n.º 2 (2011) p. 271-287.0037-1912http://hdl.handle.net/10400.21/2108In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and 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 semidirectproduct of two of its remarkable submonoids.engBilateral Semidirect ProductsTransformation SemigroupsFree MonoidsPresentationsPreserving MappingsSemigroupsPresentationsEndomorphismChainjournal article