<?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%">Dimitrova, I.</style></author><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Koppitz, J.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A note on generators of the endomorphism semigroup of an infinite countable chain</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Algebra and its Applications (DOI: 10.1142/S0219498817500311)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1142/S0219498817500311 </style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">1750031 (9 pages)</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this note, we consider the semigroup $O(X)$ of all order endomorphisms of an infinite chain $X$ and the subset $J$ of $O(X)$ of all transformations $\alpha$ such that $|Im(\alpha)|=|X|$. For an infinite countable chain $X$, we give a necessary and sufficient condition on $X$ for $O(X) = &amp;lt; J &amp;gt;$ to hold. We also present a sufficient condition on $X$ for $O(X) = &amp;lt; J &amp;gt;$ to hold, for an arbitrary infinite chain $X$. &lt;/p&gt;
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