| Title:
|
A duality for isotropic median algebras (English) |
| Author:
|
Ploščica, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
541-550 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish categorical dualities between varieties of isotropic median algebras and suitable categories of operational and relational topological structures. We follow a general duality theory of B.A. Davey and H. Werner. The duality results are used to describe free isotropic median algebras. If the number of free generators is less than five, the description is detailed. (English) |
| Keyword:
|
median algebra |
| Keyword:
|
duality |
| MSC:
|
06B99 |
| MSC:
|
06C05 |
| MSC:
|
06E15 |
| MSC:
|
08B20 |
| MSC:
|
18A40 |
| idZBL:
|
Zbl 0766.08006 |
| idMR:
|
MR1209295 |
| . |
| Date available:
|
2009-01-08T17:58:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118521 |
| . |
| Reference:
|
[1] Bandelt H.J., Hedlíková J.: Median algebras.Discrete Math. 45 1-30 (1983). MR 0700848 |
| Reference:
|
[2] Davey B.A., Werner H.: Dualities and equivalences for varieties of algebras.Coll. Math. Soc. János Bolyai 33 (Contributions to lattice theory), North-Holland, 1983,pp. 101-276. Zbl 0532.08003, MR 0724265 |
| Reference:
|
[3] Draškovičová H.: Varieties of modular median algebras.Contributions to General Algebra 7 Holder-Pichler-Tempsky Wien (1991), 119-125. MR 1143073 |
| Reference:
|
[4] Fried E., Pixley A.F.: The dual discriminator function in universal algebra.Acta Sci. Math. (Szeged) 41 (1979), 83-100. Zbl 0395.08001, MR 0534502 |
| Reference:
|
[5] Isbell J.R.: Median algebra.Trans. Amer. Math. Soc. 260 (1980), 319-362. Zbl 0446.06007, MR 0574784 |
| Reference:
|
[6] Werner H.: A duality for weakly associative lattices.Coll. Math. Soc. János Bolyai 28 (Finite algebra and multiple-valued logic), North-Holland, 1982, pp. 781-808. Zbl 0477.06004, MR 0648644 |
| Reference:
|
[7] Werner H.: A duality for the lattice variety generated by $M_3$.Coll. Math. Soc. János Bolyai 43 (Lectures in universal algebra), North-Holland, 1986, pp. 561-572. MR 0860283 |
| . |
