Partially Ordered, Primitive Regular Semigroups

Abstract

<p>The theory of partially ordered, primitive regular semigroups is developed under the hypothesis that the partial order admits enough integral idempotents. This is done in analogy to the theory of partially ordered groups. In particular, results are given which -in a purely algebraic way - determine the existence of partial orders and characterize the semigroup of integral elements of a directed, primitive regular semigroup.</p>