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

Right subdirectly irreducible completely 0-simple semigroups and uniform acts over rectangular bands