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Reference.org
Regular semigroup
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a regular semigroup is a <a href="/facts/Semigroup/rgSdk2kt">semigroup</a> <i>S</i> in which every element is regular, i.e., for each element <i>a</i> in <i>S</i> there exists an element <i>x</i> in <i>S</i> such that <i>axa</i> = <i>a</i>. Regular semigroups are one of the most-studied classes of semigroups, and their structure is particularly amenable to study via <a href="/facts/Green%2527s_relations/WIcMsL7c">Green's relations</a>. </p>