Abstract
We generalize theory of Lawson for 0 -bisimple inverse monoids to wider classes of 0 -bisimple regular semigroups. We give a necessary and sufficient condition for a 0 -bisimple R-unipotent semigroup to admit a 0-restricted idempotent-pure prehomomorphism to a primitive inverse semigroup. Several illustrations of the theory are obtained as an application of the results in this paper.
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