×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI arXiv