<?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%">Jesus, M. M.</style></author><author><style face="normal" font="default" size="100%">B. Singha</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On orientation-preserving transformations of a chain</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Algebra (DOI 10.1080/00927872.2020.1870996)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1080/00927872.2020.1870996</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">49</style></volume><pages><style face="normal" font="default" size="100%">2300-2325</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we introduce the notion of an orientation-preserving transformation on an arbitrary chain, as&lt;br /&gt;
a natural extension for infinite chains of the well known concept for finite chains introduced in 1998 by McAlister and, independently, in 1999 by Catarino and Higgins.&lt;br /&gt;
We consider the monoid POP(X) of all orientation-preserving partial transformations on a finite or infinite chain X and its submonoids OP(X) and POPI(X) of all orientation-preserving full transformations and of all orientation-preserving partial permutations on X, respectively.&lt;br /&gt;
The monoid PO(X) of all order-preserving partial transformations on X and its injective counterpart POI(X) are also considered.&lt;br /&gt;
We study the regularity and give descriptions of the Green's relations of the monoids POP(X), PO(X), OP(X), POPI(X) and POI(X).  &lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">6</style></issue></record></records></xml>