VARIETIES GENERATED BY COMPLETELY 0-SIMPLE SEMIGROUPS
Norman R. Reilly · Journal of the Australian Mathematical Society · 2008
Abstract Kublanovsky has shown that if a subvariety V of the variety RS n generated by completely 0-simple semigroups over groups of exponent n is itself generated by completely 0-simple semigroups, then it must satisfy one of three conditions: (i) A2 ∈ V ; (ii) $N_1 ot \in {\mathbf {V}};$ (iii) B2∈ V but $A_{0} ot \in {\mathbf {V}}.$ The conditions (i) and (ii) are also sufficient conditions. In this note, we complete Kublanovsky’s programme by refining condition (iii) to obtain a complete set of conditions that are both necessary and sufficient.