%0 Journal Article
%J Semigroup Forum
%D 2011
%T Bilateral semidirect product decompositions of transformation monoids.
%A Fernandes, VĂtor H.
%A Quinteiro, Teresa M.
%K bilateral semidirect products
%K free monoids
%K presentations
%K transformation semigroups
%P 271-287
%R 10.1007/s00233-011-9290-1
%V 82
%X 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.