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On simple and semisimple quantales

David Kruml·Jan Paseka
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Abstract

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.

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David Kruml, Jan Paseka. 2002-09-27. On simple and semisimple quantales. https://arxiv.org/abs/math/0209385

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