ON THE RANK OF COMPLETELY 0-SIMPLE SEMIGROUPS

Connected completely 0-simple semigroups are defined by a number of eq uivalent conditions, and a formula for the rank of these semigroups is proved. As a consequence an alternative proof of the result from [11] is given. In the case of a Rees matrix semigroup M0 [G, I, A, P] the rank is expressed in terms of \I\, \LAMBDA\, G and a certain subgroup of G depending on P. At the end the minimal rank of all semigroups M0[ G, I, LAMBDA, P] is found for a given group G. Since every completely simple semigroup is connected, every result has a corollary for these semigroups.