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De Morgan’s laws for the frame of filters of a residuated lattice
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DOI：10.1016/j.fss.2026.110036.png)
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Abstract
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In this paper, we investigate the relationship between the frame of filters of a residuated lattice and the frame of open subsets of its prime spectrum of prime filters endowed with the Stone topology. We then provide an effective characterization of the connected components of the prime spectrum of a residuated lattice. By introducing the notions of the intersection Boolean property and the join Boolean property, we obtain characterizations of residuated lattices satisfying these properties as well as De Morgan’s laws. Among other results, we characterize those residuated lattices in which every proper filter can be expressed (uniquely) as a finite intersection of comaximal prime filters. Several further related results are also derived.
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