On simple and semisimple quantales

Details On simple and semisimple quantales On simple and semisimple quantales

2002-09-27

arxiv.org/abs/math/0209385v1

Topology Atlas Invited Contributions vol. 7, no. 2 (2002) 13 pp

Mathematics

Operator Algebras

14 pages

Scientific paper

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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