## Characterizing spatial quantales.(English)Zbl 0837.46055

It is shown that an idempotent right-sided quantale [cf. C. J. Mulvey, Rend. Circ. Mat. Palermo II. Ser. Suppl., No. 12, 99-104 (1986; Zbl 0633.46065)] is spatial iff it is a subquantale of a product of simple quantales.

### MSC:

 46L89 Other “noncommutative” mathematics based on $$C^*$$-algebra theory 46L60 Applications of selfadjoint operator algebras to physics 06F05 Ordered semigroups and monoids

### Keywords:

idempotent right-sided quantale

Zbl 0633.46065
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### References:

 [1] Borceux, F., Rosick?, J. andvan den Bossche, G.,Quantales and C *-algebras, J. London Math. Soc.40 (1989), 398-404. · Zbl 0705.06009 [2] Mulvey, C. J., Suppl. Rend. Circ. Mat. Palermo, ser II,12 (1986), 99-104. [3] Rosenthal, K. J.,Quantales and Their Applications, Pitman, 1990. · Zbl 0703.06007
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