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arXiv · 2501.07673

Maximal $d$-spectra via Priestley duality

G. Bezhanishvili·P. Bhattacharjee·S. D. Melzer
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Abstract

We use Priestley duality as a new tool to study maximal $d$-spectra of arithmetic frames, both with and without units. We pay special attention to when the maximal $d$-spectrum is compact or Hausdorff. Various necessary and sufficient conditions are given, including a construction of an arithmetic frame with a unit whose maximal $d$-spectrum is not Hausdorff, thus resolving an open problem in the literature.

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G. Bezhanishvili, P. Bhattacharjee, S. D. Melzer. 2025-01-13. Maximal $d$-spectra via Priestley duality. https://doi.org/10.1142/s0219498827500058

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