Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
lattice; convex sublattice; variety
lattice; convex sublattice; variety
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 $CSub\,(\text{\bf V})=\text{\bf V}$.
References:
[1] Grätzer G.: General Lattice Theory. Birkhäuser Verlag, 1978. MR 0504338
[2] Adams M.E., Sichler J.: Lattices with unique complementation. Pacif. J. Math. 92 (1981), 1-13. MR 0618040 | Zbl 0468.06005
[3] McKenzie R.: Equational bases for lattice theories. Math. Scand. 27 (1970), 24-38. MR 0274353 | Zbl 0307.08001
[4] Wille R.: Primitive subsets of lattices. Alg. Universalis 2 (1972), 95-98. MR 0311524 | Zbl 0269.06001
Search
Partner of
