On simple and semisimple quantales

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Authors

KRUML David PASEKA Jan

Year of publication 2002
Type Article in Proceedings
Conference Topology Atlas Invited Contributions
MU Faculty or unit

Faculty of Science

Citation
Web http://at.yorku.ca/t/a/i/c/46.htm
Field General mathematics
Keywords simple quantale; semisimple quantale
Description 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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