Completion of a half linearly cyclically ordered group

Štefan Černák

Discussiones Mathematicae - General Algebra and Applications (2002)

  • Volume: 22, Issue: 1, page 5-23
  • ISSN: 1509-9415

Abstract

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The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.

How to cite

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Štefan Černák. "Completion of a half linearly cyclically ordered group." Discussiones Mathematicae - General Algebra and Applications 22.1 (2002): 5-23. <http://eudml.org/doc/287746>.

@article{ŠtefanČernák2002,
abstract = {The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.},
author = {Štefan Černák},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {dedekind cut; cyclically ordered group; lc-group; half lc-group; completion of a half lc-group; Dedekind cut},
language = {eng},
number = {1},
pages = {5-23},
title = {Completion of a half linearly cyclically ordered group},
url = {http://eudml.org/doc/287746},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Štefan Černák
TI - Completion of a half linearly cyclically ordered group
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 1
SP - 5
EP - 23
AB - The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.
LA - eng
KW - dedekind cut; cyclically ordered group; lc-group; half lc-group; completion of a half lc-group; Dedekind cut
UR - http://eudml.org/doc/287746
ER -

References

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  1. [1] Š. Černák, On the completion of cyclically ordered groups, Math. Slovaca 41 (1991), 41-49. Zbl0771.06007
  2. [2] M. Giraudet and F. Lucas, Groupes à moitié ordonnés, Fund. Math. 139 (1991), 75-89. 
  3. [3] J. Jakubík, On half cyclically ordered groups, Czechoslovak Math. J. (to appear). Zbl1010.06013
  4. [4] J. Jakubík and Š. Černák, Completion of a cyclically ordered group, Czechoslovak Math. J. 37 (112) (1987), 157-174. Zbl0624.06021
  5. [5] V. Novák, Cuts in cyclically ordered sets, Czechoslovak Math. J. 34 (109) (1984), 322-333. Zbl0551.06002
  6. [6] V. Novák and M. Novotný, On completion of cyclically ordered sets, Czechoslovak Math. J. 37 (112) (1987), 407-414. Zbl0636.06004
  7. [7] A. Quilliot, Cyclic orders, Europan J. Combin. 10 (1989), 477-488. Zbl0692.05059
  8. [8] L. Rieger, On ordered and cyclically ordered groups. I, II, and III, (Czech), Věstník Královské České Společnosti Nauk. Třida Matemat.-Přirodovĕd. 1946, no. 6, p. 1-31, 1947, no 1, p. 1-33, 1948, no. 1, p. 1-26. 
  9. [9] S. Świerczkowski, On cyclically ordered groups, Fundamenta Math. 47 (1959), 161-166. Zbl0096.01501

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