Generating sets of completely 0-simple semigroups

A formula for the rank of an arbitrary finite completely 0-simple semigroup, represented as a Rees matrix semigroup M-0[G ; I , Lambda; P], is given. The result generalizes that of Ruskuc concerning the rank of connected finite completely 0-simple semigroups. The rank is expressed in terms of vertical bar I vertical bar, vertical bar Lambda vertical bar, the number of connected components k of P, and a number r(min), which we define. We go on to show that the number r(min) is expressible in terms of a family of subgroups of G , the members of which are in one-to-one correspondence with, and determined by the nonzero entries of, the components of P . A number of applications are given, including a generalization of a result of Gomes and Howie concerning the rank of an arbitrary Brandt semigroup B ( G ,{1,..., n }).