On the Power Pseudovariety $\mathbf{PCS}$

Abstract

The pseudovariety $\mathbf{PCS}$ which is generated by all power semigroups of finite completely simple semigroups is characterized in various ways. For example, the equalities

$$\mathbf{PCS}=\mathbf{J}\malcab \mathbf{CS} =\mathbf{BG}\malcab \mathbf{RB}$$

are established. This resolves a problem raised by Kaďourek and leads to several transparent algorithms for deciding membership in $\mathbf{PCS}$.