<?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%">Delgado, Manuel</style></author><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Rees quotients of numerical semigroups</style></title><secondary-title><style face="normal" font="default" size="100%">Portugaliae Mathematica</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.ems-ph.org/journals/show_abstract.php?issn=0032-5155&amp;vol=70&amp;iss=2&amp;rank=1</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">70</style></volume><pages><style face="normal" font="default" size="100%">93-112</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We introduce a class of finite semigroups obtained by considering Rees&lt;br /&gt;
quotients of numerical semigroups.&lt;br /&gt;
  Several natural questions concerning this class, as well as particular&lt;br /&gt;
subclasses obtained by considering some special ideals, are answered while&lt;br /&gt;
others remain open. We exhibit nice presentations for these semigroups and&lt;br /&gt;
prove that the Rees quotients by ideals of N, the positive integers under&lt;br /&gt;
addition, constitute a set of generators for the pseudovariety of commutative&lt;br /&gt;
and nilpotent semigroups.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><notes><style face="normal" font="default" size="100%">&lt;p&gt;DOI: 10.4171/PM/1927&lt;/p&gt;
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