Primitive quantales

Published in Accepted in Journal of Algebra and Its Applications, 2026

Joint work with Elena Caviglia and Amartya Goswami.

We generalize Jacobson’s notion of primitive ring to the setting of quantales. We show that every primitive ring gives rise to a primitive quantale of ideals. We then prove a density theorem for strongly primitive quantales. Furthermore, we show that primitive quantales are prime and commutative strongly primitive quantales are field quantales.