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arXiv · 2506.08124

Primitive quantales

Amartya Goswami·Elena Caviglia·Luca Mesiti
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Abstract

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.

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Amartya Goswami, Elena Caviglia, Luca Mesiti. 2025-06-09. Primitive quantales. https://arxiv.org/abs/2506.08124

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