<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><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 Semigroup Cross-Sections and Complete Rewriting Systems</style></title><secondary-title><style face="normal" font="default" size="100%">International Conference on Theoretical and Mathematical Foundations of Computer Science, TMFCS-08, Orlando, Florida, USA, July 7-10, 2008</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><pages><style face="normal" font="default" size="100%">59–63</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we obtain a [finite] complete rewriting system defining a semigroup/monoid S, from a given finite&lt;br /&gt;
right cross-section of a subsemigroup/submonoid defined by a [finite] complete presentation. In the semigroup case the subsemigroup must have a right identity element which must also be part of the cross-section. In the monoid case the submonoid and the cross-section must include the identity of the semigroup. The result on semigroups allow us to show that if G is a group defined by a [finite] complete rewriting system then the completely simple semigroup M[G; I, J; P] is also defined by a [finite] complete rewriting system.&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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