# A duality for isotropic median algebras

Commentationes Mathematicae Universitatis Carolinae (1992)

- Volume: 33, Issue: 3, page 541-550
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topPloščica, Miroslav. "A duality for isotropic median algebras." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 541-550. <http://eudml.org/doc/247372>.

@article{Ploščica1992,

abstract = {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.},

author = {Ploščica, Miroslav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {median algebra; duality; categorical duality; varieties; explicit representations of the dual category; topological relational algebras; isotropic median algebras; free isotropic median algebra},

language = {eng},

number = {3},

pages = {541-550},

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

title = {A duality for isotropic median algebras},

url = {http://eudml.org/doc/247372},

volume = {33},

year = {1992},

}

TY - JOUR

AU - Ploščica, Miroslav

TI - A duality for isotropic median algebras

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1992

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

VL - 33

IS - 3

SP - 541

EP - 550

AB - 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.

LA - eng

KW - median algebra; duality; categorical duality; varieties; explicit representations of the dual category; topological relational algebras; isotropic median algebras; free isotropic median algebra

UR - http://eudml.org/doc/247372

ER -

## References

top- Bandelt H.J., Hedlíková J., Median algebras, Discrete Math. 45 1-30 (1983). (1983) MR0700848
- 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. Zbl0532.08003MR0724265
- Draškovičová H., Varieties of modular median algebras, Contributions to General Algebra 7 Holder-Pichler-Tempsky Wien (1991), 119-125. (1991) MR1143073
- Fried E., Pixley A.F., The dual discriminator function in universal algebra, Acta Sci. Math. (Szeged) 41 (1979), 83-100. (1979) Zbl0395.08001MR0534502
- Isbell J.R., Median algebra, Trans. Amer. Math. Soc. 260 (1980), 319-362. (1980) Zbl0446.06007MR0574784
- 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. Zbl0477.06004MR0648644
- 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. MR0860283

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.