<?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%">J. Araújo</style></author><author><style face="normal" font="default" size="100%">Malheiro, A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On finite complete presentations and exact decompositions of semigroups.</style></title><secondary-title><style face="normal" font="default" size="100%">Commun. Algebra</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1080/00927872.2010.514314</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">10</style></number><publisher><style face="normal" font="default" size="100%">Taylor &amp; Francis, Philadelphia, PA</style></publisher><volume><style face="normal" font="default" size="100%">39</style></volume><pages><style face="normal" font="default" size="100%">3866–3878</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove that given a finite (zero) exact right decomposition (M, T) of a semigroup S, if M is defined by a finite complete presentation, then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence, we deduce that any Zappa–Szép extension of a monoid defined by a finite complete presentation, by a finite monoid, is also defined by such a presentation.&lt;/p&gt;
&lt;p&gt;It is also proved that a semigroup M^0[A; I, J; P], where A and P satisfy some very general conditions, is also defined by a finite complete presentation.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
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