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Title: A note on convex sublattices of lattices (English)
Author: Slavík, Václav
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 36
Issue: 1
Year: 1995
Pages: 7-9
Category: math
Summary: Let $CSub\,(\text{\bf K})$ denote the variety of lattices generated by convex sublattices of lattices in $\text{\bf K}$. For any proper variety $\text{\bf V}$, the variety $CSub\,(\text{\bf V})$ is proper. There are uncountably many varieties $\text{\bf V}$ with $CSub\,(\text{\bf V})=\text{\bf V}$. (English)
Keyword: lattice
Keyword: convex sublattice
Keyword: variety
MSC: 06B20
MSC: 06B25
idZBL: Zbl 0821.06007
idMR: MR1334407
Date available: 2009-01-08T18:15:31Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Grätzer G.: General Lattice Theory.Birkhäuser Verlag, 1978. MR 0504338
Reference: [2] Adams M.E., Sichler J.: Lattices with unique complementation.Pacif. J. Math. 92 (1981), 1-13. Zbl 0468.06005, MR 0618040
Reference: [3] McKenzie R.: Equational bases for lattice theories.Math. Scand. 27 (1970), 24-38. Zbl 0307.08001, MR 0274353
Reference: [4] Wille R.: Primitive subsets of lattices.Alg. Universalis 2 (1972), 95-98. Zbl 0269.06001, MR 0311524


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