Primitive quantales
In this paper, 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.
Authors
- Elena Caviglia
- Luca Mesiti (ORCID: https://orcid.org/0009-0003-7762-1550)
- Amartya Goswami (ORCID: https://orcid.org/0000-0003-4829-0847)
Institutions
- University of Johannesburg (ZA)
- Stellenbosch University (ZA)
- National Institute for Theoretical Physics (ZA)
Publication Details
- Journal
- Journal of Algebra and Its Applications
- Published
- 2026-06-17
- DOI
- https://doi.org/10.1142/s0219498827502550
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00