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Embeddings of quantales into simple quantales. (English) Zbl 0962.06018
This nicely written article shows that any quantale is embeddable in a simple quantale by utilizing the simple quantale $$\text{End} (L)$$ of endomorphisms of a sup-lattice $$L$$ (under composition). If we begin with an involutive quantale, it can be embedded in an $$I$$-simple involutive quantale. By developing the theory of bicommutants for involutive quantales, the authors prove a quantale-theoretic analogue of von Neumann’s bicommutant theorem for $$C^*$$-algebras.

##### MSC:
 06F07 Quantales
##### Keywords:
simple quantale; involutive quantale; bicommutants
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