On simple and semisimple quantales
Operator Algebras
2007-05-23 v1
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.
Cite
@article{arxiv.math/0209385,
title = {On simple and semisimple quantales},
author = {David Kruml and Jan Paseka},
journal= {arXiv preprint arXiv:math/0209385},
year = {2007}
}
Comments
14 pages