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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2605.17274 |
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| _version_ | 1866911691783012352 |
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| author | Cenker, V. Chajda, I. Kühr, J. Länger, H. |
| author_facet | Cenker, V. Chajda, I. Kühr, J. Länger, H. |
| contents | We investigate (quasi)varieties of lattices with complementation, i.e., complemented lattices equipped with a fixed complementation as a unary operation. We focus on subclasses satisfying additional conditions, such as the quasi-identity $({x'\wedge y\approx 0} \;\&\; {x\wedge y'\approx 0})$ $\Rightarrow x\approx y$, modularity, or De Morgan's laws. We present a construction resembling a semidirect product that yields infinitely many finite subdirectly irreducible modular lattices with complementation satisfying this quasi-identity. We axiomatize small varieties, each of which covers the variety of Boolean algebras, generated by certain small modular lattices with De Morgan complementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17274 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Varieties and quasivarieties of lattices with complementation Cenker, V. Chajda, I. Kühr, J. Länger, H. Rings and Algebras We investigate (quasi)varieties of lattices with complementation, i.e., complemented lattices equipped with a fixed complementation as a unary operation. We focus on subclasses satisfying additional conditions, such as the quasi-identity $({x'\wedge y\approx 0} \;\&\; {x\wedge y'\approx 0})$ $\Rightarrow x\approx y$, modularity, or De Morgan's laws. We present a construction resembling a semidirect product that yields infinitely many finite subdirectly irreducible modular lattices with complementation satisfying this quasi-identity. We axiomatize small varieties, each of which covers the variety of Boolean algebras, generated by certain small modular lattices with De Morgan complementation. |
| title | Varieties and quasivarieties of lattices with complementation |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2605.17274 |