# A note on convex sublattices of lattices

Commentationes Mathematicae Universitatis Carolinae (1995)

- Volume: 36, Issue: 1, page 7-9
- ISSN: 0010-2628

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topSlavík, Václav. "A note on convex sublattices of lattices." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 7-9. <http://eudml.org/doc/247734>.

@article{Slavík1995,

abstract = {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 $CSub\,(\text\{\bf V\})=\text\{\bf V\}$.},

author = {Slavík, Václav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {lattice; convex sublattice; variety; variety of lattices; convex sublattices},

language = {eng},

number = {1},

pages = {7-9},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A note on convex sublattices of lattices},

url = {http://eudml.org/doc/247734},

volume = {36},

year = {1995},

}

TY - JOUR

AU - Slavík, Václav

TI - A note on convex sublattices of lattices

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1995

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 36

IS - 1

SP - 7

EP - 9

AB - 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 $CSub\,(\text{\bf V})=\text{\bf V}$.

LA - eng

KW - lattice; convex sublattice; variety; variety of lattices; convex sublattices

UR - http://eudml.org/doc/247734

ER -

## References

top- Grätzer G., General Lattice Theory, Birkhäuser Verlag, 1978. MR0504338
- Adams M.E., Sichler J., Lattices with unique complementation, Pacif. J. Math. 92 (1981), 1-13. (1981) Zbl0468.06005MR0618040
- McKenzie R., Equational bases for lattice theories, Math. Scand. 27 (1970), 24-38. (1970) Zbl0307.08001MR0274353
- Wille R., Primitive subsets of lattices, Alg. Universalis 2 (1972), 95-98. (1972) Zbl0269.06001MR0311524

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