caa a22 4500 445344946 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00233-011-9290-1 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9290-1 Bilateral semidirect product decompositions oftransformation monoids [Elektronische Daten] [Vítor Fernandes, Teresa Quinteiro] 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. Springer Science+Business Media, LLC, 2011 Bilateral semidirect products nationallicence Transformation semigroups nationallicence Free monoids nationallicence Presentations nationallicence Fernandes Vítor Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte da Caparica, 2829-516, Caparica, Portugal aut Quinteiro Teresa Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, 1950-062, Lisbon, Portugal aut Semigroup Forum Springer-Verlag 82/2(2011-04-01), 271-287 0037-1912 82:2<271 2011 82 233 https://doi.org/10.1007/s00233-011-9290-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9290-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fernandes Vítor Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte da Caparica, 2829-516, Caparica, Portugal aut NATIONALLICENCE 700 1- Quinteiro Teresa Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro 1, 1950-062, Lisbon, Portugal aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 82/2(2011-04-01), 271-287 0037-1912 82:2<271 2011 82 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer