<?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%">Preeyanuch Honyam</style></author><author><style face="normal" font="default" size="100%">Quinteiro, Teresa M.</style></author><author><style face="normal" font="default" size="100%">Boorapa Singha</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On semigroups of orientation-preserving transformations with restricted range</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Algebra (DOI:10.1080/00927872.2014.975345)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.tandfonline.com/doi/pdf/10.1080/00927872.2014.975345</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/vhf/files/opnyv2.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">44</style></volume><pages><style face="normal" font="default" size="100%">253-264</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let $X_n$ be a chain with n elements ($n\in\N$) and let $\OP_n$ be the monoid of all orientation-preserving transformations of $X_n$.  In this paper, for any nonempty subset $Y$ of $X_n$, we consider the subsemigroup $\OP_n(Y)$ of $\OP_n$ of all transformations with range contained in $Y$: we describe the largest regular subsemigroup of $\OP_n(Y)$, which actually coincides with its subset of all regular elements, and Green's relations on $\OP_n(Y)$. Also, we determine when two semigroups of the type $\OP_n(Y)$ are isomorphic and calculate their ranks. Moreover, a parallel study is presented for the correspondent subsemigroups of the monoid $\OR_n$ of all either orientation-preserving or orientation-reversing transformations of $X_n$. &lt;/p&gt;
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