On simple and semisimple quantales
| Authors | |
|---|---|
| Year of publication | 2002 |
| Type | Article in Proceedings |
| Conference | Topology Atlas Invited Contributions |
| MU Faculty or unit | |
| 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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