  In a recent paper, J. W. Pelletier and J. Rosicky published a
characterization of *-simple *-quantales. Their results were adapted for the
case of simple quantales by J. Paseka. In this paper we present similar
characterizations which do not use a notion of discrete quantale. We also show
a completely new characterization based on separating and cyclic sets. Further
we explain a link to simple quantale modules. To apply these characterizations,
we study (*-)semisimple (*-)quantales and discuss some other perspectives. Our
approach has connections with several earlier works on the subject.
