<?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 endomorphisms of a chain with restricted range</style></title><secondary-title><style face="normal" font="default" size="100%">Semigroup Forum (DOI: 10.1007/s00233-013-9548-x)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/article/10.1007%2Fs00233-013-9548-x</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">89</style></volume><pages><style face="normal" font="default" size="100%">77-104</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let $X$ be a finite or infinite chain and let $\O(X)$ be the monoid of all  endomorphisms of $X$.&lt;br /&gt;
In this paper, we describe the largest regular subsemigroup of $\O(X)$ and Green's relations on $\O(X)$.&lt;br /&gt;
In fact, more generally, if $Y$ is a nonempty subset of $X$ and $\O(X,Y)$ is the subsemigroup of $\O(X)$ of all elements with range contained in $Y$,&lt;br /&gt;
we characterize the largest regular subsemigroup of $\O(X,Y)$ and Green's relations on $\O(X,Y)$.&lt;br /&gt;
Moreover, for finite chains, we determine when two semigroups of the type $\O(X,Y)$ are isomorphic and calculate their ranks. &lt;/p&gt;
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