Convex lines in median groups

Milan Kolibiar

Archivum Mathematicum (1992)

  • Volume: 028, Issue: 1-2, page 67-75
  • ISSN: 0044-8753

Abstract

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There is proved that a convex maximal line in a median group G , containing 0, is a direct factor of G .

How to cite

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Kolibiar, Milan. "Convex lines in median groups." Archivum Mathematicum 028.1-2 (1992): 67-75. <http://eudml.org/doc/247343>.

@article{Kolibiar1992,
abstract = {There is proved that a convex maximal line in a median group $G$, containing 0, is a direct factor of $G$.},
author = {Kolibiar, Milan},
journal = {Archivum Mathematicum},
keywords = {median algebra; group; line; direct product; ternary operation; median group; median algebra; betweenness preserving injective mapping; direct factor decomposition; convex maximal line},
language = {eng},
number = {1-2},
pages = {67-75},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Convex lines in median groups},
url = {http://eudml.org/doc/247343},
volume = {028},
year = {1992},
}

TY - JOUR
AU - Kolibiar, Milan
TI - Convex lines in median groups
JO - Archivum Mathematicum
PY - 1992
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 028
IS - 1-2
SP - 67
EP - 75
AB - There is proved that a convex maximal line in a median group $G$, containing 0, is a direct factor of $G$.
LA - eng
KW - median algebra; group; line; direct product; ternary operation; median group; median algebra; betweenness preserving injective mapping; direct factor decomposition; convex maximal line
UR - http://eudml.org/doc/247343
ER -

References

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  1. Median algebras, Discrete Math. 45 (1983), 1-30. (1983) MR0700848
  2. Chains in modular ternary latticoids, Math. Slovaca 27 (1977), 249-256. (1977) MR0536142
  3. Median algebra, Trans. Amer. Math. Soc. 260 (1980), 319-362. (1980) Zbl0446.06007MR0574784
  4. A ternary operation in distributive lattices, Bull. Amer. Math. Soc. 53 (1947), 749-752. (1947) Zbl0031.25002MR0021540
  5. Median groups, Archivum Math. (Brno) 25 (1989), 73-82. (1989) Zbl0738.06016MR1189201
  6. Discret product decompositions of median groups, General Algebra 1988, Proceedings of the Conference in Krems (Australia), August 1988. North Holland 1990, 139-151. MR1060351
  7. Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3 (1952), 369-381. (1952) MR0048405
  8. Medians, lattices, and trees, Proc. Amer. Math. Soc. 5 (1954), 808-812. (1954) Zbl0056.26201MR0064750
  9. Groups with an operation median, Komenský University Bratislava (1977), Thesis. (1977) 

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