Primitive quantales
Rings and Algebras
2025-06-11 v1
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.
Keywords
Cite
@article{arxiv.2506.08124,
title = {Primitive quantales},
author = {Amartya Goswami and Elena Caviglia and Luca Mesiti},
journal= {arXiv preprint arXiv:2506.08124},
year = {2025}
}