Geodesic
Completely zero-simple semigroups generated by nilpotent elements
Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 163-165

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For a completely 0-simple semigroup, Howie [2] has investigated the subsemigroup generated by the idempotents. Here we determine those elements of such a semigroup which are generated by the set of nilpotent elements and hence we derive a condition for a completely 0-simple semigroup to be nilpotent generated. This condition is purely combinatorial, in terms of the structure of the graph associated with the semigroup, and it includes the case of a non-regular Rees matrix semigroup. 
Houghton, C. H.; Sullivan, R. P. Completely zero-simple semigroups generated by nilpotent elements. Glasgow mathematical journal, Tome 25 (1984) no. 2, pp. 163-165. doi: 10.1017/S0017089500005577
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[1] 1.Houghton, C. H., Completely 0-simple semigroups and their associated graphs and groups, Semigroup Forum 14 (1977), 41–67. Google Scholar | DOI

[2] 2.Howie, J. M., Idempotents in completely 0-simple semigroups, Glasgow Math. J. 19 (1978), 109–113. Google Scholar | DOI

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