  The aim of this paper is characterizing right subdirectly irreducible
completely 0-simple semigroups. We prove that such semigroups are indeed groups
with least nontrivial subgroups. On the other hand we prove that right
irreducible completely 0-simple semigroups are groups for which nontrivial
subgroups have nontrivial intersection. Ultimately, we characterize the class
of uniform acts as an overclass of subdirectly irreducible acts over
rectangular bands.
