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arXiv · 2509.11603

Kites and representations of pseudo MV-algebras

Michal Botur·Tomasz Kowalski
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Abstract

We investigate the structure of perfect residuated lattices, focussing especially on perfect pseudo MV-algebras. We show that perfect pseudo MV-algebras can be represented as a generalised version of kites of Dvure\v{c}enskij and Kowalski, and that they are categorically equivalent to $\ell$-groups with a distinguished automorphism. We then characterise varieties generated by kites and describe the lattice of these varieties as a complete sublattice of the lattice of perfectly generated varieties of perfect pseudo MV-algebras.

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Michal Botur, Tomasz Kowalski. 2025-09-15. Kites and representations of pseudo MV-algebras. https://doi.org/10.1016/j.fss.2022.09.014

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