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1. Finding the complete structure of regular semigroups of a certain class has succeeded only when sufficiently strong conditions on idempotents and/or ideals have been imposed. On the one hand, there is the theorem of Rees , giving the structure of completely 0-simple semigroups, and its successive generalizations to primitive regular semigroups , and 3-and 3i-regular semigroups . On the other hand, with very different restrictions, Reilly  has determined the structure of bisimpledoi:10.1090/s0002-9904-1971-12677-0 fatcat:ieosz3ue3ve5bam4t2ekjxpvma