Primitive quantales generalize Jacobson's primitive rings: primitive rings yield primitive quantales of ideals, primitive quantales are prime, and commutative strongly primitive quantales are exactly field quantales.
Jacobson, A topology for the set of primitive ideals in an arbitrary ring, Proc
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Primitive quantales
Primitive quantales generalize Jacobson's primitive rings: primitive rings yield primitive quantales of ideals, primitive quantales are prime, and commutative strongly primitive quantales are exactly field quantales.