| Topology Atlas Document # taic-46 | Topology Atlas Invited Contributions vol. 7 issue 2 (2002) 13 pp. |
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.
Mathematics Subject Classification: 06F07
Financial Support of the Grant Agency of the Czech Republic under
the grant No.~201/99/0310 is gratefully acknowledged.
The authors thank Mamuka Jibladze for suggestive questions given
during Quantum logic/quantale/category workshop in Brussels 10--14/4/2000,
from which the paper arose.
This article was accepted for publication in
Proceedings
of the Ninth Prague Topological Symposium, (Prague, 2001),
edited by Petr Simon, but was omitted from the final
publication due to a production error.
Date received: September 27, 2002.
Copyright © 2002 by the authors. Distributed by Topology Atlas with permission of the authors.