Abstract
In this work we treat monoidal lattices (or multiplicative semilattices, in some people’s terminology, but we stick to the terminology in [Sun, 1994]) and monoidal closed (=residuated) lattices and MV-algebras (as special cases) from the viewpoint of the theory of quantales. We use the machinery of Gabriel topologies on coherent quantales in order to describe (the locale of opens of) the prime spectrum of an MV-algebra. For that we rely heavily on results obtained in [Karazeris, 1998]. Let us introduce the types of structures we study, in a hierarchy of increasing structural complexity:
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© 1999 Springer Science+Business Media Dordrecht
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Karazeris, P. (1999). Gabriel Filters and the Spectrum of an MV-Algebra. In: Dubois, D., Prade, H., Klement, E.P. (eds) Fuzzy Sets, Logics and Reasoning about Knowledge. Applied Logic Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1652-9_10
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DOI: https://doi.org/10.1007/978-94-017-1652-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5324-4
Online ISBN: 978-94-017-1652-9
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