<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Quinteiro, Teresa M.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Bilateral semidirect product decompositions of transformation monoids.</style></title><secondary-title><style face="normal" font="default" size="100%">Semigroup Forum</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">bilateral semidirect products</style></keyword><keyword><style  face="normal" font="default" size="100%">free monoids</style></keyword><keyword><style  face="normal" font="default" size="100%">presentations</style></keyword><keyword><style  face="normal" font="default" size="100%">transformation semigroups</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><number><style face="normal" font="default" size="100%">2</style></number><volume><style face="normal" font="default" size="100%">82</style></volume><pages><style face="normal" font="default" size="100%">271-287</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract></record></records></xml>