Remarks about the Q-lattice of the variety of lattices
| Autor: | M. E. Adams, Wieslaw Dziobiak |
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| Rok vydání: | 2021 |
| Předmět: |
Modular lattice
Algebra and Number Theory Quasivariety High Energy Physics::Lattice 010102 general mathematics 0102 computer and information sciences 01 natural sciences Omega Combinatorics 010201 computation theory & mathematics Lattice (order) Free lattice 0101 mathematics Algebra over a field Variety (universal algebra) Mathematics |
| Zdroj: | Algebra universalis. 82 |
| ISSN: | 1420-8911 0002-5240 |
| DOI: | 10.1007/s00012-020-00681-7 |
| Popis: | Let L denote the Q-lattice of the variety $${\mathcal {V}}$$ of lattices, i.e. the lattice of quasivarieties that are contained in $${\mathcal {V}}$$ . Let F denote the free lattice in $${\mathcal {V}}$$ with $$\omega $$ free generators and let Q(F) denote the quasivariety of lattices generated by F. Let Fin denote the collection of finite lattices which belong to Q(F) and let Q(Fin) denote the quasivariety generated by Fin. Moreover, let $${\mathcal {M}}^{-}_{3}$$ denote the quasivariety of lattices which do not contain an isomorphic copy of $$M_3$$ (the 5-element non-distributive modular lattice) as a sublattice and let $${\mathcal {S}}$$ denote a selector of non-isomorphic finite quasicritical lattices which belong to Q(Fin). In this paper, we establish the following |
| Databáze: | OpenAIRE |
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