| Title:
|
Convex lines in median groups (English) |
| Author:
|
Kolibiar, Milan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
28 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
67-75 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
There is proved that a convex maximal line in a median group $G$, containing 0, is a direct factor of $G$. (English) |
| Keyword:
|
median algebra |
| Keyword:
|
group |
| Keyword:
|
line |
| Keyword:
|
direct product |
| MSC:
|
06F15 |
| MSC:
|
08A99 |
| MSC:
|
20F60 |
| MSC:
|
20N10 |
| MSC:
|
51A25 |
| idZBL:
|
Zbl 0783.20038 |
| idMR:
|
MR1201867 |
| . |
| Date available:
|
2008-06-06T21:04:50Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107437 |
| . |
| Reference:
|
[1] Bandelt H.J. and Hedlíková J.: Median algebras.Discrete Math. 45 (1983), 1-30. MR 0700848 |
| Reference:
|
[2] Hedlíková J.: Chains in modular ternary latticoids.Math. Slovaca 27 (1977), 249-256. MR 0536142 |
| Reference:
|
[3] Isbell J.R.: Median algebra.Trans. Amer. Math. Soc. 260 (1980), 319-362. Zbl 0446.06007, MR 0574784 |
| Reference:
|
[4] Kiss S.A.: A ternary operation in distributive lattices.Bull. Amer. Math. Soc. 53 (1947), 749-752. Zbl 0031.25002, MR 0021540 |
| Reference:
|
[5] Kolibiar M.: Median groups.Archivum Math. (Brno) 25 (1989), 73-82. Zbl 0738.06016, MR 1189201 |
| Reference:
|
[6] Kolibiar M.: Discret product decompositions of median groups.General Algebra 1988, Proceedings of the Conference in Krems (Australia), August 1988. North Holland 1990, 139-151. MR 1060351 |
| Reference:
|
[7] Sholander M.: Trees, lattices, order, and betweenness.Proc. Amer. Math. Soc. 3 (1952), 369-381. MR 0048405 |
| Reference:
|
[8] Sholander M.: Medians, lattices, and trees.Proc. Amer. Math. Soc. 5 (1954), 808-812. Zbl 0056.26201, MR 0064750 |
| Reference:
|
[9] Marcisová T.: Groups with an operation median.Komenský University Bratislava (1977), Thesis. |
| . |
