Kites and representations of pseudo MV-algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914037928820736 |
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| author | Botur, Michal Kowalski, Tomasz |
| author_facet | Botur, Michal Kowalski, Tomasz |
| contents | 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 Dvurečenskij 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kites and representations of pseudo MV-algebras Botur, Michal Kowalski, Tomasz Logic 06D35 (Primary) 06F15 (Secondary) 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 Dvurečenskij 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. |
| title | Kites and representations of pseudo MV-algebras |
| topic | Logic 06D35 (Primary) 06F15 (Secondary) |
| url | https://arxiv.org/abs/2509.11603 |